Solve for p
p=3
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5\times 2^{p}=40
Use the rules of exponents and logarithms to solve the equation.
2^{p}=8
Divide both sides by 5.
\log(2^{p})=\log(8)
Take the logarithm of both sides of the equation.
p\log(2)=\log(8)
The logarithm of a number raised to a power is the power times the logarithm of the number.
p=\frac{\log(8)}{\log(2)}
Divide both sides by \log(2).
p=\log_{2}\left(8\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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