Question

Find the value of $x$ in exponents and powers when the $2^{x+1}\times 2^5=2^7$.

Answer 1

Compute the required value:

Given: $2^{x+1}\times 2^5=2^7$

By laws of exponents, we know;

$a^m\times a^n=a^{m+n}$

If the bases are the same, we can add the powers.

$$\begin{gathered} \Rightarrow 2^{x+1}\times 2^5=2^7 \\ \Rightarrow x+1+5=7 \\ \Rightarrow x+6=7 \\ \Rightarrow x=1 \end{gathered}$$

Hence, the value of $x$ is $1$.