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How do you find the inverse of $y = {log}_{6} (x + 2)$ $y= log_6 (x+2)$ ?

1 Answer

Oct 13, 2016

$x = 6^{y} - 2$ $x=6^y-2$

Explanation:

Start with the basic equivalence:
$XXX c = {log}_{b} a \Leftrightarrow a = b^{c}$ $color(white)("XXX")c=log_b a hArr a=b^c$

Therefore
$XXX y = {log}_{6} (x + 2) \Leftrightarrow 6^{y} = x + 2$ $color(white)("XXX")y=log_6(x+2) hArr 6^y=x+2$

From which it follows that
$XXX 6^{y} - 2 = x$ $color(white)("XXX")6^y-2=x$

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