What is the inverse of ln(e^x-1)-ln(2)-1 ?

The inverse of ln(e^x-1)-ln(2)-1 is ln(2e^{x+1}+1)

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inverse of ln(e^x-1)-ln(2)-1

inverse

ln (e^{x} - 1) - ln (2) - 1

ln (2 e^{x + 1} + 1)

Solution steps

y = ln (e^{x} - 1) - ln (2) - 1

Replace

x

with

y

x = ln (e^{y} - 1) - ln (2) - 1

Solve for

y, x = ln (e^{y} - 1) - ln (2) - 1

ln (2 e^{x + 1} + 1)

f (x) = x^{4} - 6 x^{2}

3 x - 2 y = 12

f (x) = \frac{1}{( x - 3 )}

(1, 4), (2, 2)

y = - x^{2} - 3

What is the inverse of ln(e^x-1)-ln(2)-1 ?
The inverse of ln(e^x-1)-ln(2)-1 is ln(2e^{x+1}+1)