How do you find the inverse of #y=log_5 (x+2) #?

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Answer 1 · 2018-04-12T15:59:39

#f^-1(x)=5^x-2#

To find the inverse we need to express #x# as a function of #y#.

By the definition of the logarithm:

If:

#y=log_b(a)#

Then:

#b^y=a#

From example:

#y=log_5(x+2)=>5^y=x+2#

#x=5^y-2#

Substituting:

#y=x#

#y=5^x-2#

#f^-1(x)=5^x-2#