Simplify \({8}^{5}\) to \(32768\).
\[{2}^{x}\times {2}^{x+3}=32768\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{2}^{x+x+3}=32768\]
Simplify \(x+x+3\) to \(2x+3\).
\[{2}^{2x+3}=32768\]
Convert both sides to the same base.
\[{2}^{2x+3}={2}^{15}\]
Cancel the base of \(2\) on both sides.
\[2x+3=15\]
Subtract \(3\) from both sides.
\[2x=15-3\]
Simplify \(15-3\) to \(12\).
\[2x=12\]
Divide both sides by \(2\).
\[x=\frac{12}{2}\]
Simplify \(\frac{12}{2}\) to \(6\).
\[x=6\]
x=6
