What is the answer to ln(x)+ln(x+1)=2 ?

The answer to ln(x)+ln(x+1)=2 is x=(-1+sqrt(1+4e^2))/2

Solve for x: ln(x)+ln(x+1)=2

The solution is x=(-1+sqrt(1+4e^2))/2

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ln (x) + ln (x + 1) = 2

x = \frac{- 1 + 1 + 4 e ^{2}}{2}

Decimal Notation

x = 2.26388 \dots

Solution steps

ln (x) + ln (x + 1) = 2

Apply log rules

x (x + 1) = e^{2}

Solve

x (x + 1) = e^{2} : x = \frac{- 1 + 1 + 4 e ^{2}}{2}, x = \frac{- 1 - 1 + 4 e ^{2}}{2}

x = \frac{- 1 + 1 + 4 e ^{2}}{2}, x = \frac{- 1 - 1 + 4 e ^{2}}{2}

Verify Solutions:

x = \frac{- 1 + 1 + 4 e ^{2}}{2}

True

, x = \frac{- 1 - 1 + 4 e ^{2}}{2}

False

The solution is

x = \frac{- 1 + 1 + 4 e ^{2}}{2}

1.85 = - lo g_{10} (x)

lo g_{x} (0.1) = - \frac{1}{3}

10 lo g_{10} (x) = 26.5

lo g_{4} (3 x^{2} + 6 x + 7) = 2

ln (ln (5 x)) = 0

What is the answer to ln(x)+ln(x+1)=2 ?
The answer to ln(x)+ln(x+1)=2 is x=(-1+sqrt(1+4e^2))/2
Solve for x: ln(x)+ln(x+1)=2
The solution is x=(-1+sqrt(1+4e^2))/2