Question

$7^{2{\log }_{7}5}=$

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

Answer 1

The correct option is C

$25$

Explanation for the correct option:

Use the logarithmic relation to simplify the expression.

Given: $7^{2{\log }_{7}5}$

Shift $2$ inside the logarithm.

$\begin{array}{rcl}{7}^{2{\log }_{7}5}& =& 7^{l{\mathrm{og}}_7{5}^2}\\ & =& 7^{{\log }_{7}25}\end{array}$ $\left[\because \mathrm{alogb}={\mathrm{logb}}^a\right]$

$\begin{array}{rcl}& =& 7^{{\log }_{7}25}=25\end{array}$ $\left[\because a^{lo{g}_{a}b}=b\right]$

Hence, option (C) is the correct answer.