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

The answer to ln(2x+1)=2-ln(x) is x=(-1+sqrt(1+8e^2))/4

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

The solution is x=(-1+sqrt(1+8e^2))/4

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

x = \frac{- 1 + 1 + 8 e ^{2}}{4}

Decimal Notation

x = 1.68830 \dots

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

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

Solve

(2 x + 1) x = e^{2} : x = \frac{- 1 + 1 + 8 e ^{2}}{4}, x = \frac{- 1 - 1 + 8 e ^{2}}{4}

x = \frac{- 1 + 1 + 8 e ^{2}}{4}, x = \frac{- 1 - 1 + 8 e ^{2}}{4}

Verify Solutions:

x = \frac{- 1 + 1 + 8 e ^{2}}{4}

True

, x = \frac{- 1 - 1 + 8 e ^{2}}{4}

False

The solution is

x = \frac{- 1 + 1 + 8 e ^{2}}{4}

lo g_{x} (6 - 5 x) = 2

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

7.5 = - lo g_{10} (x)

ln (3) - ln (x + 5) - ln (x) = 0

lo g_{x} (\frac{1}{4}) = - 1

What is the answer to ln(2x+1)=2-ln(x) ?
The answer to ln(2x+1)=2-ln(x) is x=(-1+sqrt(1+8e^2))/4
Solve for x: ln(2x+1)=2-ln(x)
The solution is x=(-1+sqrt(1+8e^2))/4