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

The answer to 2ln(x+2)-ln(x)=ln(2x-1) is x=(5+sqrt(41))/2

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

The solution is x=(5+sqrt(41))/2

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

x = \frac{5 + 41}{2}

Decimal Notation

x = 5.70156 \dots

Solution steps

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

Apply log rules

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

Solve

(x + 2)^{2} = (2 x - 1) x : x = - \frac{- 5 + 41}{2}, x = \frac{5 + 41}{2}

x = - \frac{- 5 + 41}{2}, x = \frac{5 + 41}{2}

Verify Solutions:

x = - \frac{- 5 + 41}{2}

False

, x = \frac{5 + 41}{2}

True

The solution is

x = \frac{5 + 41}{2}

lo g_{3} (x - 1) = - 1

ln (x) - ln (2) = 0

2^{4} = 16 lo g_{2} (x)

lo g_{2} (4 x - 12) = 5

ln (6 x) + ln (4) = ln (6 x + 7)

What is the answer to 2ln(x+2)-ln(x)=ln(2x-1) ?
The answer to 2ln(x+2)-ln(x)=ln(2x-1) is x=(5+sqrt(41))/2
Solve for x: 2ln(x+2)-ln(x)=ln(2x-1)
The solution is x=(5+sqrt(41))/2