What is the inverse of f(x)=log_{2}((e^x-6)/4) ?

The inverse of f(x)=log_{2}((e^x-6)/4) is ln(2^{x+2}+6)

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inverse of f(x)=log_{2}((e^x-6)/4)

inverse

f (x) = lo g_{2} (\frac{e ^{x} - 6}{4})

ln (2^{x + 2} + 6)

Solution steps

y = lo g_{2} (\frac{e ^{x} - 6}{4})

Replace

x

with

y

x = lo g_{2} (\frac{e ^{y} - 6}{4})

Solve for

y, x = lo g_{2} (\frac{e ^{y} - 6}{4})

ln (2^{x + 2} + 6)

What is the inverse of f(x)=log_{2}((e^x-6)/4) ?
The inverse of f(x)=log_{2}((e^x-6)/4) is ln(2^{x+2}+6)