Solve for p
p = \frac{3}{2} = 1\frac{1}{2} = 1.5
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6^{2p}=216
Use the rules of exponents and logarithms to solve the equation.
\log(6^{2p})=\log(216)
Take the logarithm of both sides of the equation.
2p\log(6)=\log(216)
The logarithm of a number raised to a power is the power times the logarithm of the number.
2p=\frac{\log(216)}{\log(6)}
Divide both sides by \log(6).
2p=\log_{6}\left(216\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
p=\frac{3}{2}
Divide both sides by 2.
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