How do you find the inverse of #y=log_5(x+4)+1#?

1 Answer
Gió
Nov 30, 2015

I found: #y=5^(x-1)-4#

Explanation:

I would try to isolate #x# on one side by first moving #1# and then changing the log into an exponential as:
#log_5(x+4)=y-1#
#x+4=5^(y-1)#
#x=5^(y-1)-4#

Now I switch places to give it a more "friendly-function" aspect:
#y=5^(x-1)-4#

Graphically you have:
#y=log_5(x+4)+1# (red)
#y=5^(x-1)-4# (blue)

enter image source here

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