What is the answer to ln(x)+ln(x+1)=5 ?

The answer to ln(x)+ln(x+1)=5 is x=(-1+sqrt(1+4e^5))/2

Solve for x: ln(x)+ln(x+1)=5

The solution is x=(-1+sqrt(1+4e^5))/2

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ln (x) + ln (x + 1) = 5

x = \frac{- 1 + 1 + 4 e ^{5}}{2}

Decimal Notation

x = 11.69275 \dots

Solution steps

ln (x) + ln (x + 1) = 5

Apply log rules

x (x + 1) = e^{5}

Solve

x (x + 1) = e^{5} : x = \frac{- 1 + 1 + 4 e ^{5}}{2}, x = \frac{- 1 - 1 + 4 e ^{5}}{2}

x = \frac{- 1 + 1 + 4 e ^{5}}{2}, x = \frac{- 1 - 1 + 4 e ^{5}}{2}

Verify Solutions:

x = \frac{- 1 + 1 + 4 e ^{5}}{2}

True

, x = \frac{- 1 - 1 + 4 e ^{5}}{2}

False

The solution is

x = \frac{- 1 + 1 + 4 e ^{5}}{2}

ln (x - 3) - ln (x - 5) = ln (5)

ln (x) + 2 = 0

lo g_{2 x + 3} (81) = 2

ln (2 x - 3) - ln (x + 1) = e

lo g_{10} ((x + 2)^{2}) = 2

What is the answer to ln(x)+ln(x+1)=5 ?
The answer to ln(x)+ln(x+1)=5 is x=(-1+sqrt(1+4e^5))/2
Solve for x: ln(x)+ln(x+1)=5
The solution is x=(-1+sqrt(1+4e^5))/2