KCET · Maths · Basic of Mathematics
\(7^{2 \log _{7} 5}\) is equal to
- A \(\log _{7} 35\)
- B 5
- C 25
- D \(\log _{7} 25\)
Answer & Solution
Correct Answer
(C) 25
Step-by-step Solution
Detailed explanation
Given, \(7^{2 \log _{7} 5}\)
\[
\begin{aligned}
&=7^{\log _{7}(5)^{2}} \quad\left[\because a^{\log _{a} x}=x, x>0, x \neq 0,1\right] \\
&=(5)^{2}=25
\end{aligned}
\]
\[
\begin{aligned}
&=7^{\log _{7}(5)^{2}} \quad\left[\because a^{\log _{a} x}=x, x>0, x \neq 0,1\right] \\
&=(5)^{2}=25
\end{aligned}
\]
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