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:

$y=x$

$y=5^x-2$

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

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