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JAMB Mathematics 2019 Paper

Question : 64

Total: 73

Evaluate

\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}

Solution:

Concept:

Use the logarithmic rule

\log_a a^k = k

after rewriting each number as a power of the logarithm base.

Explanation:

Start with the given expression:

\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}

Rewrite

9

81

, and

625

in index form:

9 = 3^2

81 = 3^4

, and

625 = 5^4

Substitute these into the expression:

\frac{2\log_{3} 3^2 \times \log_{3} (3^4)^{-2}}{\log_{5} 5^4}

Simplify the exponent:

(3^4)^{-2} = 3^{-8}

Use

\log_a a^k = k

for each term:

2\log_{3} 3^2 = 2 \times 2 = 4

\log_{3} 3^{-8} = -8

\log_{5} 5^4 = 4

Now substitute these values back:

\frac{4 \times (-8)}{4} = -8

Therefore, the correct answer is

-8

Answer:

-8

(Option C)

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