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

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

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

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

x = \frac{e + 1}{e - 1}

Decimal

x = 2.16395 \dots

Solution steps

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

Add

ln (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 1 = e (x - 1)

Solve

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

x = \frac{e + 1}{e - 1}

Verify Solutions:

x = \frac{e + 1}{e - 1}

True

The solution is

x = \frac{e + 1}{e - 1}

- 8 lo g_{10} (3 x) + 9 = 11

x, lo g_{3} (x + y) = z

x = 9 - ln (2 x)

lo g_{- 2 x - 3} (2 x^{2} - 2 x - 15) = 2

x, lo g_{3} (x) = 3

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