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

The answer to ln(x)+ln(x+1)=3 is x=(-1+sqrt(1+4e^3))/2

Solve for x: ln(x)+ln(x+1)=3

The solution is x=(-1+sqrt(1+4e^3))/2

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

x = \frac{- 1 + 1 + 4 e ^{3}}{2}

Decimal

x = 4.00949 \dots

Solution steps

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

Apply log rules

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

Solve

x (x + 1) = e^{3} : x = \frac{- 1 + 1 + 4 e ^{3}}{2}, x = \frac{- 1 - 1 + 4 e ^{3}}{2}

x = \frac{- 1 + 1 + 4 e ^{3}}{2}, x = \frac{- 1 - 1 + 4 e ^{3}}{2}

Verify Solutions:

x = \frac{- 1 + 1 + 4 e ^{3}}{2}

True

, x = \frac{- 1 - 1 + 4 e ^{3}}{2}

False

The solution is

x = \frac{- 1 + 1 + 4 e ^{3}}{2}

0 = 2 ln (x - 2)

lo g_{2} (4 x + 5) = 3

lo g_{2} (4 x + 5) = 5

lo g_{9} (1.5 x) = 3

lo g_{2} (x^{2}) = 5

What is the answer to ln(x)+ln(x+1)=3 ?
The answer to ln(x)+ln(x+1)=3 is x=(-1+sqrt(1+4e^3))/2
Solve for x: ln(x)+ln(x+1)=3
The solution is x=(-1+sqrt(1+4e^3))/2