Question

Write y = 8^x as a logarithmic function.
A. log8x = y
B. logx8 = y
C. log8y = x
D. logy8 = x

Answer 1

First, take logarithms of both sides:
\[y = 8^x\]\[\log y = \log8^x\]Then use the law of logarithms which states that loga^b = bloga to get:
\[\log y = x\log8\]Then rearrange to get:
\[x = \frac{ \log y }{ \log8 }\]

Answer 2

Whoops, forgot to tell you that the logarithms are to the base 8, so you can simplify to
\[x=\log_{8}y\]So the answer is C.