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

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

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

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

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

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

Decimal

x = 2.26388 \dots

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

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

Solve

(x + 1) x = 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}

lo g_{2} (x) - 1 = lo g_{2} (x - 16)

ln (x) = 5 - x

ln (x) = - 17

ln (2 x) = 7 x + 8

6 ln (x) - 3 = 2 - ln (x)

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