How do you find the inverse of $y = {log}_{5} (x + 2)$ $y=log_5 (x+2)$ ?

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Answer 1 · 2018-04-12T15:59:39

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

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

By the definition of the logarithm:

If:

$y = {log}_{b} (a)$ $y=log_b(a)$

Then:

$b^{y} = a$ $b^y=a$

From example:

$y = {log}_{5} (x + 2) \Rightarrow 5^{y} = x + 2$ $y=log_5(x+2)=>5^y=x+2$

$x = 5^{y} - 2$ $x=5^y-2$

Substituting:

$y = x$ $y=x$

$y = 5^{x} - 2$ $y=5^x-2$

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

How do you find the inverse of y=log5(x+2)y=log_5 (x+2) ?