What is the inverse of #y= log_(1/2) (x+4)# ?

1 Answer
Mar 4, 2018

Answer:

The inverse is #y=(1/2)^x-4#

Explanation:

To find the inverse, switch #x# with #y# and vice versa, then solve for #y#. To convert out of #log# form, make it exponential form.

#color(white)=>y=log_(1/2)(x+4)#

#=>color(red)x=log_color(blue)(1/2)color(green)((y+4))#

#color(white)=>color(green)(y+4)=color(blue)((1/2))^color(red)x#

#color(white)=>y=(1/2)^x-4#

Here's a diagram of the graphs (I included the line #y=x# to show the reflection):

https://www.desmos.com/calculator