Sure, let's solve the equation given:
[tex]\[ \sqrt{2^{x+5}} = 16 \][/tex]
Here's the step-by-step solution:
1. Square both sides to eliminate the square root:
[tex]\[
(\sqrt{2^{x+5}})^2 = 16^2
\][/tex]
This simplifies to:
[tex]\[
2^{x+5} = 256
\][/tex]
2. Rewrite 256 as a power of 2:
[tex]\[
256 = 2^8
\][/tex]
So the equation becomes:
[tex]\[
2^{x+5} = 2^8
\][/tex]
3. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[
x + 5 = 8
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x + 5 = 8
\][/tex]
[tex]\[
x = 8 - 5
\][/tex]
[tex]\[
x = 3
\][/tex]
Therefore, the solution is:
[tex]\[
x = 3
\][/tex]
