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Solve for x
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Solve for x (complex solution)
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2^{x+3}=128
Use the rules of exponents and logarithms to solve the equation.
\log(2^{x+3})=\log(128)
Take the logarithm of both sides of the equation.
\left(x+3\right)\log(2)=\log(128)
The logarithm of a number raised to a power is the power times the logarithm of the number.
x+3=\frac{\log(128)}{\log(2)}
Divide both sides by \log(2).
x+3=\log_{2}\left(128\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
x=7-3
Subtract 3 from both sides of the equation.