What is the inverse of ln(2x-3)-ln(x+5)+1 ?

The inverse of ln(2x-3)-ln(x+5)+1 is (-3e-5e^x)/(e^x-2e)

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inverse of ln(2x-3)-ln(x+5)+1

inverse

ln (2 x - 3) - ln (x + 5) + 1

\frac{- 3 e - 5 e ^{x}}{e ^{x} - 2 e}

Solution steps

y = ln (2 x - 3) - ln (x + 5) + 1

Replace

x

with

y

x = ln (2 y - 3) - ln (y + 5) + 1

Solve for

y, x = ln (2 y - 3) - ln (y + 5) + 1

\frac{- 3 e - 5 e ^{x}}{e ^{x} - 2 e}

What is the inverse of ln(2x-3)-ln(x+5)+1 ?
The inverse of ln(2x-3)-ln(x+5)+1 is (-3e-5e^x)/(e^x-2e)