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

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

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

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

x = 6

Solution steps

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

Add

ln (x - 4)

to both sides

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

Simplify

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

Apply log rules

x (x - 4) = x + 6

Solve

x (x - 4) = x + 6 : x = 6, x = - 1

x = 6, x = - 1

Verify Solutions:

x = 6

True

, x = - 1

False

The solution is

x = 6

x, y x = - lo g_{10} (x)

0.78215 = 0.6446 ln (x) - 0.5557

- lo g_{10} (x) = 7

4 ln (4.6 x) = 7

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

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