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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = - \frac{9}{8 x}

\frac{1}{x} + 1

f (x) = 4 (x - 1)^{3} + 2

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

\frac{4}{1 + ln ( 1 + e ^{x} )}

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