Evaluate \( \dfrac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625} \)
Question 1 Report
Evaluate \( \dfrac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625} \)
Answer Details
We can simplify the expression using the properties of logarithms.
First, we can rewrite the expression as:
2log3(3^2) * log3(3^4) - 2log5(5^4)
Using the power rule of logarithms, we can simplify the first term:
2log3(3^2) * log3(3^4) = 2(2) * 4 = 16
Using the power rule of logarithms again, we can simplify the second term:
2log5(5^4) = 8log5(5) = 8
Substituting these simplified terms back into the original expression, we get:
16 - 8 = 8
Therefore, the value of the expression is 8, which is option (C) in the given choices.
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