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

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

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

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

Popular >

ln (x + 1) - ln (x - 1) = \frac{1}{2}

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

Decimal

x = 4.08298 \dots

Solution steps

ln (x + 1) - ln (x - 1) = \frac{1}{2}

Add

ln (x - 1)

to both sides

ln (x + 1) - ln (x - 1) + ln (x - 1) = \frac{1}{2} + ln (x - 1)

Simplify

ln (x + 1) = \frac{1}{2} + ln (x - 1)

Apply log rules

x + 1 = e (x - 1)

Solve

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

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

Verify Solutions:

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

True

The solution is

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

8 lo g_{10} (10 x + 5) = 16

2 (4 x ln (x) + 2 x) = 0

lo g_{12} (x) + lo g_{12} (11 x - 1) = 1

ln (\frac{t - 20}{200}) = - 0.11 t

lo g_{e} (x - 8) = 5

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