



 
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  


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