Hi Nancy,

For any positive base $b$ the log base $b$ function, $f(x) = \log_b(x)$ and the exponential function, $g(x) = b^x$ are inverses. This means that

\[f(g(x)) = x \mbox{ and } g(f(x)) = x\]

thus

\[\log_b(b^x) = x \mbox{ and } b^{\log_b(x)} = x.\]

You have $b = 8$ and hence if you raise both sides of $log_8(P) = 7$ to the power of 8, on the left you get

\[8^{\log_8(P)} = P\]

and on the right you get

\[7^8 .\]

Penny