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

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

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

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

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

Solution steps

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

Add

ln (x - 2)

to both sides

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

Simplify

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

Apply log rules

x + 2 = e (x - 2)

Solve

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

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

Verify Solutions:

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

True

The solution is

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

(x + 1) = lo g_{10} (x - 1) + 3

lo g_{4} (x + 20) = 3

ln (x) - ln (x + 1) = 5

5 = lo g_{3} (x^{2} + 18)

ln (x - 1) - 1 = 0

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