What is the inverse of 3ln(sqrt(x+4)-1),x>0 ?

The inverse of 3ln(sqrt(x+4)-1),x>0 is e^{(2x)/3}+2e^{x/3}-3

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inverse of 3ln(sqrt(x+4)-1),x>0

inverse

3 ln (x + 4 - 1), x > 0

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

Solution steps

y = 3 ln (x + 4 - 1)

Replace

x

with

y

x = 3 ln (y + 4 - 1)

Solve for

y, x = 3 ln (y + 4 - 1)

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

What is the inverse of 3ln(sqrt(x+4)-1),x>0 ?
The inverse of 3ln(sqrt(x+4)-1),x>0 is e^{(2x)/3}+2e^{x/3}-3