What is the inverse of f(x)=ln(3x-5)-ln(x+9)+5,x>= 2 ?

The inverse of f(x)=ln(3x-5)-ln(x+9)+5,x>= 2 is (-5e^5-9e^x)/(e^x-3e^5)

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inverse of f(x)=ln(3x-5)-ln(x+9)+5,x>= 2

inverse

f (x) = ln (3 x - 5) - ln (x + 9) + 5, x \geq 2

\frac{- 5 e ^{5} - 9 e ^{x}}{e ^{x} - 3 e ^{5}}

Solution steps

y = ln (3 x - 5) - ln (x + 9) + 5

Replace

x

with

y

x = ln (3 y - 5) - ln (y + 9) + 5

Solve for

y, x = ln (3 y - 5) - ln (y + 9) + 5

\frac{- 5 e ^{5} - 9 e ^{x}}{e ^{x} - 3 e ^{5}}

What is the inverse of f(x)=ln(3x-5)-ln(x+9)+5,x>= 2 ?
The inverse of f(x)=ln(3x-5)-ln(x+9)+5,x>= 2 is (-5e^5-9e^x)/(e^x-3e^5)