What is the answer to ln(x+3)-ln(x-1)=ln(x) ?

The answer to ln(x+3)-ln(x-1)=ln(x) is x=3

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

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

x = 3

Solution steps

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

Add

ln (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 3 = x (x - 1)

Solve

x + 3 = x (x - 1) : x = 3, x = - 1

x = 3, x = - 1

Verify Solutions:

x = 3

True

, x = - 1

False

The solution is

x = 3

lo g_{2} (x^{3}) = 6

lo g_{10} (x^{2} - x - 6) - x = lo g_{0} (n + 8) - 4 (2)

lo g_{2} (a^{2} - 5) = 2

lo g_{x} (20) + lo g_{x} (5) = 2

lo g_{3} (lo g_{2} (x + 9)) = 1

What is the answer to ln(x+3)-ln(x-1)=ln(x) ?
The answer to ln(x+3)-ln(x-1)=ln(x) is x=3
Solve for x: ln(x+3)-ln(x-1)=ln(x)
The solution is x=3