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

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

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

inverse

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

\frac{1 - 5 e ^{x}}{2 e ^{x} - 3}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{1 - 5 e ^{x}}{2 e ^{x} - 3}

f (x) = \frac{3 x - 2}{2 x + 5}

f (x) = \frac{4}{x + 8}

f (x) = \frac{4}{x + 5}

\frac{0.5 z}{z - 1}

y = 5 x - 6

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