Question

Find the value of $x$ if: $8^{255}={32}^x$

Answer 1

Compute the required value of $x$:

$$\begin{gathered} \Rightarrow 8^{255}={32}^x \\ \Rightarrow {\left(2^3\right)}^{255}={\left(2^5\right)}^x \\ \Rightarrow 2^{765}=2^{5x} \\ \Rightarrow 765=5x \\ \Rightarrow \frac{765}{5}=x \\ \Rightarrow x=153 \end{gathered}$$

Hence, the value of $x$ is $153$.