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

The answer to ln(x-6)=ln(x+6)-ln(x-4) is x=9

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

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

x = 9

Solution steps

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

Add

ln (x - 4)

to both sides

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

Simplify

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

Apply log rules

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

Solve

(x - 6) (x - 4) = x + 6 : x = 9, x = 2

x = 9, x = 2

Verify Solutions:

x = 9

True

, x = 2

False

The solution is

x = 9

0.63 = ln (x)

lo g_{5} (x) - 1 = 6 lo g_{x} (5)

ln ((x + 2)^{2}) = 6

lo g_{4} (3 x - 4) + lo g_{4} (x + 6) = 2

lo g_{3} (x + 7) = 4

What is the answer to ln(x-6)=ln(x+6)-ln(x-4) ?
The answer to ln(x-6)=ln(x+6)-ln(x-4) is x=9
Solve for x: ln(x-6)=ln(x+6)-ln(x-4)
The solution is x=9