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

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

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

inverse

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

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

Solution steps

y = 5 ln (\frac{x + 2}{3})

Replace

x

with

y

x = 5 ln (\frac{y + 2}{3})

Solve for

y, x = 5 ln (\frac{y + 2}{3})

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

f (x) = \frac{( 2 x - 5 )}{( x + 7 )}

f (x) = 3 x + 6

\frac{x + 2}{x - 5}

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

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