What is the answer to solvefor x,f^{-1}(x)=ln(x+3) ?

The answer to solvefor x,f^{-1}(x)=ln(x+3) is x=-\W(-1/(e^{3/f)f})f-3

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solvefor x,f^{-1}(x)=ln(x+3)

solve for

x, f^{- 1} (x) = ln (x + 3)

x = - W (- \frac{1}{e ^{\frac{3}{f}} f}) f - 3

Solution steps

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

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{f^{- 1} x} = e^{l n (x + 3)}

Simplify

e^{f^{- 1} x} : e^{\frac{x}{f}}

Simplify

e^{l n (x + 3)} : x + 3

e^{\frac{x}{f}} = x + 3

Solve

e^{\frac{x}{f}} = x + 3 : x = - W (- \frac{1}{e ^{\frac{3}{f}} f}) f - 3

x = - W (- \frac{1}{e ^{\frac{3}{f}} f}) f - 3

Verify Solutions:

x = - W (- \frac{1}{e ^{\frac{3}{f}} f}) f - 3

True

The solution is

x = - W (- \frac{1}{e ^{\frac{3}{f}} f}) f - 3

8 + ln (8 x) = 26 - 2 ln (x)

3 = 8 lo g_{10} (6 x + 3)

0 = 2 x ln (2 x) + x

lo g_{10} (\frac{4 x}{2}) = 2

4 ln (7 x - 8) - 13 = - 25

What is the answer to solvefor x,f^{-1}(x)=ln(x+3) ?
The answer to solvefor x,f^{-1}(x)=ln(x+3) is x=-\W(-1/(e^{3/f)f})f-3