What is the inverse equation of y=10^x

Question

What is the inverse equation of
`y=10^x`

Answer 1

Explanation:

`y = 10 {}^(x)`

Swap y and x

`x = 10 {}^(y)`

The opposite of a exponent with base b, is a logarithm with base b.

`log_(10)(x) = log_(10)(10 {}^(y) )`

By definition, since log and exponent are inverses of each other and they have the same bases. This composition will spit out the variable , y

`log_(10)(x) = y`

Using notation

`f {}^( - 1) (x) = log_(10)(x)`