What is the inverse of #y=log(x-3)?# ?

1 Answer
Nov 1, 2015

Answer:

#y=10^x+3#

Explanation:

The inverse of a logarithmic function #y=log_ax# is the exponential function #y=a^x#.

#[1]" "y=log(x-3)#

First we must convert this to exponential form.

#[2]" "hArr10^y=x-3#

Isolate #x# by adding #3# to both sides.

#[3]" "10^y+3=x-3+3#

#[4]" "x=10^y+3#

Finally, switch the positions of #x# and #y# to get the inverse function.

#[5]" "color(blue)(y=10^x+3)#