Question

log5 x=-3

Answer 1

Hi, Joe, and welcome to OpenStudy!

Looks like you want to solve that equation for x.

Are you familiar with the concept of "inverse functions"?

If so, perhaps you'll recognize that y = log to the base 5 of x
and y = (base 5)^x are inverse functions.

Answer 2

0.6 @mathmale

Answer 3

You could start by writing out


5 =5

Then, taking the given equation: log5 x=-3

write
log5 x -3
5 =5

Recognize that the left side simplifies to x? and the right side to 1/(5^3) = ???

Answer 4

Thanks, @MichaelaePalmore1234 , but I'm encouraging Joe to learn the steps of solving this sort of problem by himself.

Answer 5

\(\large{ \bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}\\ \quad \\ \quad \\
log_{\color{red}{5}}{\color{blue}{ x}}=-3\implies \square^\square =\square }\)

Answer 6

\[5^{-3}=x=?\]
Nice work, Joe!