Question

Express 5^3 = x as a logarithmic equation.

Answer 1

A log is an exponent. The log of a number to a base is the exponent you need to raise the base to to get the number. For exapmple, what is the log base 2 of 8? That is the same as asking "what exponent do you raise 2 to get 8?" The answer here is 3 since 2^3 = 8, so log(base 2) 8 = 3.

Now let's look at your problem. 5 is the base. 3 is the exponent, so 3 is the log. x is the number.

`5^3 = x \Longleftrightarrow \log_5 x = 3`

In general,

`b^y = x \Longleftrightarrow \log_b x = y`

Answer 2

that would be 3 = log5 x