Q86 / 180 · KCET 2007 · Mathematics

$7^{2 \log _{7} 5}$ is equal to

  • A
    $\log _{7} 35$
  • B
    5
  • Correct answer
    C
    25
  • D
    $\log _{7} 25$

Solution

Given, $7^{2 \log _{7} 5}$ $$ \begin{aligned} &=7^{\log _{7}(5)^{2}} \quad\left[\because a^{\log _{a} x}=x, x>0, x \neq 0,1\right] \\ &=(5)^{2}=25 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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