Question

If ${17}^{\frac{1}{5}x}=289$, find the value of $x$

Answer 1

Finding the value of $x$

$\begin{array}{l}{17}^{\frac{1}{5}x}=289\\ \Rightarrow {17}^{\frac{1}{5}x}={17}^2\\ \Rightarrow \frac{1}{5}x=2\left(\text{Base are equal,so equating powers}\right)\\ \Rightarrow x=2\times 5\\ \Rightarrow x=10\end{array}$

Hence,the value of $x=10$