Which of the following lograthmic equations is equivalent to the exponential equation below?{8}^(x) = 512no explanation needed

Question

which of the following lograthmic equations is equivalent to the exponential equation below?
`{8}^(x) = 512`no explanation needed

Answer 1

By definition, the logarithm can be used equivalently in these expressions:

`\begin{gathered} b^a=c^{} \\ \log _bc=a \end{gathered}`

So, if we want an equivalent to:

`8^x=512`

We can write:

`\log _8512=x`