How do you find the inverse of #y=log_2(x+4)#?

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Answer 1 · 2016-01-11T12:37:51

#f^-1(x) = 2^x-2#

For finding the inverse follow these steps.

Step 1: Swap #x# and #y#
Step 2: Solve for #y#
Step 3: Write the result in the correct notation.

To find inverse of #y=log_2(x+4)#

Step 1: Swap #x# and #y#

#x=log_2(y+4)#

Step 2: Solve for #y#

Convert the log to exponent form.
#if log_b(a) = k# then #a=b^k#

We have #x=log_2(y+2)#
#2^x = y+2#

Subtracting #2# on both the sides.
#2^x-2 =y#

#y=2^x - 2# Inverse function

Step 3:

#f^-1(x) = 2^x-2#