What is the answer to ln(x+4)-ln(x-6)=1 ?

The answer to ln(x+4)-ln(x-6)=1 is x=(6e+4)/(e-1)

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ln(x+4)-ln(x-6)=1

ln (x + 4) - ln (x - 6) = 1

x = \frac{6 e + 4}{e - 1}

Solution steps

ln (x + 4) - ln (x - 6) = 1

Add

ln (x - 6)

to both sides

ln (x + 4) - ln (x - 6) + ln (x - 6) = 1 + ln (x - 6)

Simplify

ln (x + 4) = 1 + ln (x - 6)

Apply log rules

x + 4 = e (x - 6)

Solve

x + 4 = e (x - 6) : x = \frac{6 e + 4}{e - 1}

x = \frac{6 e + 4}{e - 1}

Verify Solutions:

x = \frac{6 e + 4}{e - 1}

True

The solution is

x = \frac{6 e + 4}{e - 1}

lo g_{2} (x + 1) = 1 - lo g_{2} (x)

lo g_{5} (4 x + 1) = 2

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

lo g_{25} (x) = \frac{- 1}{2}

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

What is the answer to ln(x+4)-ln(x-6)=1 ?
The answer to ln(x+4)-ln(x-6)=1 is x=(6e+4)/(e-1)
Solve for x: ln(x+4)-ln(x-6)=1
The solution is x=(6e+4)/(e-1)