What is the answer to ln(x+2)-ln(x-6)=1 ?

The answer to ln(x+2)-ln(x-6)=1 is x=(6e+2)/(e-1)

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ln(x+2)-ln(x-6)=1

ln (x + 2) - ln (x - 6) = 1

x = \frac{6 e + 2}{e - 1}

Decimal

x = 10.65581 \dots

Solution steps

ln (x + 2) - ln (x - 6) = 1

Add

ln (x - 6)

to both sides

ln (x + 2) - ln (x - 6) + ln (x - 6) = 1 + ln (x - 6)

Simplify

ln (x + 2) = 1 + ln (x - 6)

Apply log rules

x + 2 = e (x - 6)

Solve

x + 2 = e (x - 6) : x = \frac{6 e + 2}{e - 1}

x = \frac{6 e + 2}{e - 1}

Verify Solutions:

x = \frac{6 e + 2}{e - 1}

True

The solution is

x = \frac{6 e + 2}{e - 1}

\frac{x}{ln ( x )} = 0

lo g_{10} (x) 64 = 3

ln (x) + ln (x + 1) = 3

0 = 2 ln (x - 2)

lo g_{2} (4 x + 5) = 3

What is the answer to ln(x+2)-ln(x-6)=1 ?
The answer to ln(x+2)-ln(x-6)=1 is x=(6e+2)/(e-1)
Solve for x: ln(x+2)-ln(x-6)=1
The solution is x=(6e+2)/(e-1)