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

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

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

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

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ln (x) = - ln (x + 1)

x = \frac{- 1 + 5}{2}

Decimal Notation

x = 0.61803 \dots

Solution steps

ln (x) = - ln (x + 1)

Add

ln (x + 1)

to both sides

ln (x) + ln (x + 1) = - ln (x + 1) + ln (x + 1)

Simplify

ln (x) + ln (x + 1) = 0

Apply log rules

x (x + 1) = 1

Solve

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

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

Verify Solutions:

x = \frac{- 1 + 5}{2}

True

, x = \frac{- 1 - 5}{2}

False

The solution is

x = \frac{- 1 + 5}{2}

lo g_{2} (5 x + 1) = 4

lo g_{2} (\frac{k + 2}{3 - k}) = - 2

2.8 = - lo g_{10} (x)

lo g_{3} (x + 7) + lo g_{3} (x + 5) = 1

lo g_{b} (8) = - \frac{1}{2}

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