Question 46

Mathematics Logarithms Hard

The value of \({3}^{3-\log _35}\) is

(A) \(\frac{5}{27}\)
(B) \(\frac{27}{5}\)
(C) \(\frac{9}{5}\)
(D) \(\frac{5}{9}\)
โœ“ Correct Answer: Option B Verified Solution

๐Ÿ“˜ Step-by-Step Solution & Detailed Explanation:

\[ \begin{aligned} & \text{We know } a^{\log_a x} = x, \\ & 3^{3 - \log_3 5} = 3^3 \cdot 3^{-\log_3 5} = 3^3 \cdot 3^{\log_3 \left( \frac{1}{5} \right)}, \\ & = 27 \cdot \left( \frac{1}{5} \right) = \frac{27}{5}. \end{aligned} \]

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