What is the answer to ln(x)+ln(x+1)=4 ?

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

Solve for x: ln(x)+ln(x+1)=4

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

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ln (x) + ln (x + 1) = 4

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

Decimal

x = 6.90595 \dots

Solution steps

ln (x) + ln (x + 1) = 4

Apply log rules

x (x + 1) = e^{4}

Solve

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

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

Verify Solutions:

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

True

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

False

The solution is

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

lo g_{\frac{1}{6}} (3 - 10 x) = - 2

lo g_{10} (3 x + 1) - lo g_{10} (2 x - 3) = 1 - lo g_{10} (5)

5 x^{4} ln (x) + x^{4} = 0

\frac{ln ( 6 b )}{6} = 0

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

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