Question

Find the inverse of the exponential function f(x)=10^x

Answer 1

Answer:
`y=(ln(x))/(ln(10))`

Explanation:

To find the inverse of the function, you first replace the y with x and x with y. Then you solve for y.

`y=10^x` [replace y with x and x with y]

`x=10^y` [find natural log of both sides to get y alone]

`ln(x)=ln(10)^y` [divide ln(10) on both sides]

`(ln(x))/(ln(10)) =y`

Now that we have found y after switching y with x and x with y, we know that the inverse is
`y=(ln(x))/(ln(10))`.