What is the inverse of $y = 6^{x}$ $y=6^x$ ?

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Answer 1 · 2016-06-27T04:30:23

$x = {log}_{6} y$ $x=log_6y$

Since

$x = {log}_{b} a \Leftrightarrow a = b^{x}$ $x=log_ba iff a=b^x$

you have:

$y = 6^{x} \Leftrightarrow x = {log}_{6} y$ $y=6^x iff x=log_6y$

Answer 2 · 2016-06-27T04:30:32

$y = \frac{ln x}{ln 6}$ $y= (ln x)/(ln 6)$

Replace x with y and y with x,

$x = 6^{y}$ $x= 6^y$ and solve for y now

ln x= yln 6

$y = \frac{ln x}{ln 6}$ $y= (ln x)/(ln 6)$

Answer 3 · 2017-07-18T10:40:33

See below.

If $g (x)$ $g(x)$ is the inverse for $f (x)$ $f(x)$ then

$g (f (x)) = x$ $g(f(x))=x$ then

$g (6^{x}) = x \Rightarrow g (x) = \frac{{log}_{e} x}{{log}_{e} 6} = f^{- 1} (x)$ $g(6^x)=x rArrg(x) = log_ex/log_e 6 = f^-1(x)$ .

What is the inverse of y=6^xy=6xy=6^x?