What is the inverse of y=log(x-4)+2y=log(x4)+2 ?

1 Answer
Mar 2, 2018

10^(x-2)+410x2+4 is the inverse.

Explanation:

We have the function f(x)=y=log(x-4)+2f(x)=y=log(x4)+2

To find f^-1(x)f1(x), we take our equation:

y=log(x-4)+2y=log(x4)+2

Switch the variables:

x=log(y-4)+2x=log(y4)+2

And solve for yy:

x-2=log(y-4)x2=log(y4)

We can write x-2x2 as log(10^(x-2))log(10x2), so we have:

log(10^(x-2))=log(y-4)log(10x2)=log(y4)

As the bases are the same:

y-4=10^(x-2)y4=10x2

y=10^(x-2)+4y=10x2+4

Which is your inverse.