What is the inverse of f(x)=log_{6}(3^x) ?

The inverse of f(x)=log_{6}(3^x) is (xln(6))/(ln(3))

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inverse of f(x)=log_{6}(3^x)

inverse

f (x) = lo g_{6} (3^{x})

\frac{x ln ( 6 )}{ln ( 3 )}

Solution steps

y = lo g_{6} (3^{x})

Replace

x

with

y

x = lo g_{6} (3^{y})

Solve for

y, x = lo g_{6} (3^{y})

\frac{x ln ( 6 )}{ln ( 3 )}

y = \frac{1}{2} x - 1, (6, 2)

2 x + 8 y = 24

(x^{3} + 4 x^{2}) (6 x^{2} - 1)

f (x) = \frac{x + 6}{x ^{2} + 4 x - 12}

f (x) = 1 + x^{2}

What is the inverse of f(x)=log_{6}(3^x) ?
The inverse of f(x)=log_{6}(3^x) is (xln(6))/(ln(3))