What is the answer to ln(x)+ln(1/x+1)=3 ?

The answer to ln(x)+ln(1/x+1)=3 is x=e^3-1

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ln(x)+ln(1/x+1)=3

ln (x) + ln (\frac{1}{x} + 1) = 3

x = e^{3} - 1

Decimal

x = 19.08553 \dots

Solution steps

ln (x) + ln (\frac{1}{x} + 1) = 3

Apply log rules

x (\frac{1}{x} + 1) = e^{3}

Solve

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

x = e^{3} - 1

Verify Solutions:

x = e^{3} - 1

True

The solution is

x = e^{3} - 1

x, ln (ln (x)) = 0

lo g_{x} (336) = 2

lo g_{7} (3 - x) = 2 lo g_{7} (4)

lo g_{10} (a) = 4

lo g_{10} (x) = 40.92

What is the answer to ln(x)+ln(1/x+1)=3 ?
The answer to ln(x)+ln(1/x+1)=3 is x=e^3-1
Solve for x: ln(x)+ln(1/x+1)=3
The solution is x=e^3-1