What is the inverse of f(x)=log_{6}(2x)+log_{6}(3) ?

The inverse of f(x)=log_{6}(2x)+log_{6}(3) is 2^{x-1}*3^{-1+x}

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inverse of f(x)=log_{6}(2x)+log_{6}(3)

inverse

f (x) = lo g_{6} (2 x) + lo g_{6} (3)

2^{x - 1} \cdot 3^{- 1 + x}

Solution steps

y = lo g_{6} (2 x) + lo g_{6} (3)

Replace

x

with

y

x = lo g_{6} (2 y) + lo g_{6} (3)

Solve for

y, x = lo g_{6} (2 y) + lo g_{6} (3)

2^{x - 1} \cdot 3^{- 1 + x}

f (x) = x^{2} - 7 x

f (x) = \frac{x}{5} - \frac{3}{5}

- \frac{2}{5} x + 4

f (x) = 2 4 - x

f (x) = 5 - x - x^{2} - 9

What is the inverse of f(x)=log_{6}(2x)+log_{6}(3) ?
The inverse of f(x)=log_{6}(2x)+log_{6}(3) is 2^{x-1}*3^{-1+x}