SSS2 Maths Quiz 2.6- SIMPLE EQUATIONS WITH LOGARITHMS

Solve \(\log_{2} x = 5\).

A) 5

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B) 32

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C) 25

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D) 64

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Solve \(\log_{10} x = 2\).

A) 100

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B) 10

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C) 20

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D) 1000

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If \(\log_{3} x = 4\), find \(x\).

A) 81

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B) 64

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C) 27

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D) 243

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Solve \(\log_{5} x = -1\).

A) \(\frac{1}{25}\)

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B) 5

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C) \(\frac{1}{5}\)

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D) 25

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If \(\log_{a} x = 0\), then \(x =\)

A) \(a\)

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B) 0

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C) 1

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D) \(a^0\)

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Solve \(\log_{4} x = \frac{3}{2}\).

A) 8

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B) 16

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C) 6

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D) 4

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If \(\log_{7} x = 2\), find \(x\).

A) 14

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B) 49

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C) 21

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D) 7

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Solve \(\log_{10} x = -2\).

A) 0.1

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B) 0.01

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C) 100

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D) 10

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If \(\log_{5} x = \frac{1}{2}\), find \(x\).

A) 25

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B) 5

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C) \(\sqrt{5}\)

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D) 1

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Solve \(\log_{2} x = 0\).

A) 0

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B) 1

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C) 2

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D) 4

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The square of \(0.6\) is:

A) 0.26

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B) 0.36

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C) 0.46

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D) 0.56

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The cube of \(0.4\) is:

A) 0.064

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B) 0.16

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C) 0.24

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D) 0.32

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The square root of \(0.49\) is:

A) 0.6

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B) 0.8

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C) 0.7

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D) 0.9

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The cube root of \(0.125\) is:

A) 0.5

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B) 0.25

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C) 0.75

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D) 1.5

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Using four-figure tables, the square of \(0.87\) is approximately:

A) 0.656

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B) 0.746

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C) 0.757

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D) 0.867

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Which of the following is correct?

A) \(\sqrt{0.64} = 0.9\)

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B) \(\sqrt{0.64} = 0.8\)

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C) \(\sqrt{0.64} = 0.7\)

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D) \(\sqrt{0.64} = 0.6\)

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The cube of \(0.25\) is:

A) 0.0156

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B) 0.025

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C) 0.0625

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D) 0.125

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If \(x = 0.04\), then \(\sqrt{x}\) equals:

A) 0.2

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B) 0.4

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C) 0.6

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D) 0.8

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Using four-figure tables, \(\sqrt{0.0036}\) is approximately:

A) 0.06

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B) 0.06

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C) 0.36

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D) 0.6

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Which of the following results is correct?

A) \((0.3)^2 = 0.06\)

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B) \((0.3)^2 = 0.12\)

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C) \((0.3)^2 = 0.09\)

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D) \((0.3)^2 = 0.3\)

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Using four-figure tables, evaluate \(0.24 \times 0.36\).

A) 0.864

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B) 8.64

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C) 0.0864

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D) 0.086

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The product of \(0.48 \times 0.25\) using four-figure tables is approximately:

A) 0.012

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B) 0.48

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C) 0.120

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D) 1.20

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Find \(0.56 \times 0.32\).

A) 1.792

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B) 0.01792

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C) 0.179

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D) 0.79

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Calculate \(0.72 \div 0.09\).

A) 0.12

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B) 8.0

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C) 8

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D) 80

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Evaluate \(0.36 \div 0.12\).

A) 3

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B) 0.3

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C) 30

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D) 12

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Which of these results is correct? \(0.042 \times 0.05\)

A) 0.0021

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B) 0.021

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C) 0.21

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D) 2.1

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Evaluate \(0.84 \div 0.07\).

A) 0.12

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B) 1.2

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C) 12

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D) 120

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If \(0.25 \times 0.64 = k\), then \(k\) is:

A) 0.016

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B) 0.160

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C) 1.60

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D) 16.0

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Using four-figure tables, calculate \(0.18 \times 0.45\).

A) 0.81

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B) 0.0081

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C) 0.081

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D) 8.1

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Evaluate \(0.96 \div 0.12\).

A) 0.8

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B) 8

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C) 80

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D) 0.08

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The logarithm of a number less than 1 is always:

A) Positive

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B) Zero

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C) Undefined

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D) Negative

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The logarithm of 0.1 to base 10 is:

A) 0

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B) 1

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C) -1

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D) 10

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The logarithm of 0.01 to base 10 is:

A) 1

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B) 0

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C) -2

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D) 2

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In logarithms of numbers less than 1, the characteristic is:

A) Always zero

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B) Always positive

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C) Always negative

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D) Always greater than 1

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The logarithm of \(0.025\) to base 10 can be written as:

A) \(-1 + \log_{10} 2.5\)

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B) \(-2 + \log_{10} 2.5\)

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C) \(-3 + \log_{10} 2.5\)

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D) \(\log_{10} 25\)

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Which of the following is true about \(\log_{10} 0.2\)?

A) \(\log_{10} 0.2 = \log_{10} 2\)

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B) \(\log_{10} 0.2 = -\log_{10} 2\)

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C) \(\log_{10} 0.2 = -1 + \log_{10} 2\)

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D) \(\log_{10} 0.2 = 1 – \log_{10} 2\)

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The logarithm of 0.0005 to base 10 is:

A) \(-2 + \log_{10} 5\)

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B) \(-3 + \log_{10} 5\)

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C) \(-4 + \log_{10} 5\)

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D) \(-5 + \log_{10} 5\)

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Which part of a logarithm can be negative when the number is less than 1?

A) Mantissa

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B) Characteristic

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C) Both mantissa and characteristic

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D) Neither mantissa nor characteristic

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The logarithm of \(0.0032\) to base 10 can be written as:

A) \(-2 + \log_{10} 3.2\)

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B) \(-3 + \log_{10} 3.2\)

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C) \(-3 + \log_{10} 3.2\)

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D) \(-4 + \log_{10} 3.2\)

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The characteristic of \(\log_{10} 0.006\) is:

A) -1

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B) -2

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C) -3

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D) -4

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The logarithm of a number greater than 1 has a characteristic that is:

A) Negative

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B) Fractional

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C) Positive

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D) Zero

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The characteristic of \( \log_{10} 25 \) is:

A) 0

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B) 2

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C) 1

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D) 3

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To find \( \log_{10} 4.56 \) using a four-figure table, you look up:

A) 456 in the table

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B) 45 in the table, then use mean difference for 6

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C) 4.56 directly in the table

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D) 400 in the table

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The mantissa of a logarithm is always:

A) Negative

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B) Greater than 1

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C) Positive and less than 1

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D) An integer

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If \( \log_{10} 2 = 0.3010 \), then \( \log_{10} 20 \) is:

A) 0.3010

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B) 1.3010

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C) 2.3010

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D) 3.3010

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The number of digits in a number \( N \) is given by:

A) The mantissa of \( \log N \)

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B) The characteristic of \( \log N \) + 1

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C) The reciprocal of \( \log N \)

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D) The integer part of the mantissa

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The characteristic of \( \log_{10} 567 \) is:

A) 2

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B) 3

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C) 1

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D) 0

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Which part of a logarithm is obtained directly from the four-figure table?

A) The mantissa

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B) The characteristic

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C) Both characteristic and mantissa

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D) The integer part

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If \( \log_{10} 3 = 0.4771 \), then \( \log_{10} 300 \) is:

A) 0.4771

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B) 1.4771

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C) 2.4771

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D) 3.4771

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Which of the following is correct about logarithms?

A) \( \log_{10} 1 = 1 \)

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B) \( \log_{10} 10 = 1 \)

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C) \( \log_{10} 100 = 1 \)

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D) \( \log_{10} 0 = 0 \)

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Simplify \(10^2 \times 10^3\)

\(10^5\)

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\(10^6\)

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\(10^4\)

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\(10^7\)

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What is the number \[7.4 \times 10^3 \] in ordinary form?

740

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7400

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74

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0.0074

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Which of the following is \( 602,000,000,000,000,000,000,000 \) written correctly in standard form?

\( 6.02 \times 10^{23} \)

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\( 6.02 \times 10^{22} \)

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\( 60.2 \times 10^{23} \)

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\( 602 \times 10^{21} \)

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How is the number \( 0.00000567 \) written in standard form?

\( 5.67 \times 10^{-5} \)

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\( 5.67 \times 10^{-6} \)

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\( 567 \times 10^{-8} \)

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\( 56.7 \times 10^{-7} \)

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Simplify \(\frac{15 \times 10^4 }{ 3 \times 10^{-2}}\)

\(5 \times 10^6\)

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\(5 \times 10^2\)

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\(5 \times 10^8\)

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\(5 \times 10^{10}\)

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Calculate \((3.1 \times 10^4) \times (2.0 \times 10^2)\). Give your answer in standard form.

\( 62 \times 10^6 \)

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\( 6.2 \times 10^6 \)

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\( 6.2 \times 10^8 \)

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\( 5.1 \times 10^6 \)

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Calculate \(\frac{(8.4\times 10^7)}{2.1 \times 10^2)}\). Give your answer in standard form.

\( 4.0 \times 10^5 \)

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\( 4.0 \times 10^9 \)

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\( 4.0 \times 10^3 \)

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\( 4.0 \times 10^6 \)

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Calculate \( (5.5 \times 10^3) + (4.5 \times 10^2) \). Give your answer in standard form.

\( 1.0 \times 10^4 \)

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\( 10.0 \times 10^5 \)

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\( 5.95 \times 10^3 \)

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\( 5.95 \times 10^2 \)

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The radius of a hydrogen atom is approximately \( 2.5 \times 10^{-11} \) meters. How is this written in ordinary form?

0.000000000025 m

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0.00000000025 m

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0.0000000025 m

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0.000000025 m

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Subtract \( 3.2 \times 10^4 \) from \( 7.1 \times 10^4 \). Give your answer in standard form.

\( 3.9 \times 10^0 \)

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\( 3.9 \times 10^8 \)

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\( 3.9 \times 10^4 \)

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\( -3.9 \times 10^4 \)

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SSS2 Maths Quiz 2.6- SIMPLE EQUATIONS WITH LOGARITHMS

SSS2 Maths Quiz 2.6- SIMPLE EQUATIONS WITH LOGARITHMS

Noah Wasiu September 14, 2025

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