What is the inverse of f(x)=6log_{5}(2x-6) ?

The inverse of f(x)=6log_{5}(2x-6) is (5^{x/6}+6)/2

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inverse of f(x)=6log_{5}(2x-6)

inverse

f (x) = 6 lo g_{5} (2 x - 6)

\frac{5 ^{\frac{x}{6}} + 6}{2}

Solution steps

y = 6 lo g_{5} (2 x - 6)

Replace

x

with

y

x = 6 lo g_{5} (2 y - 6)

Solve for

y, x = 6 lo g_{5} (2 y - 6)

\frac{5 ^{\frac{x}{6}} + 6}{2}

What is the inverse of f(x)=6log_{5}(2x-6) ?
The inverse of f(x)=6log_{5}(2x-6) is (5^{x/6}+6)/2