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

The answer to ln(x+1)-ln(x-2)=ln(x) is x=(3+sqrt(13))/2

Solve for x: ln(x+1)-ln(x-2)=ln(x)

The solution is x=(3+sqrt(13))/2

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

x = \frac{3 + 13}{2}

Solution steps

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

Add

ln (x - 2)

to both sides

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

Simplify

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

Apply log rules

x + 1 = x (x - 2)

Solve

x + 1 = x (x - 2) : x = \frac{3 + 13}{2}, x = \frac{3 - 13}{2}

x = \frac{3 + 13}{2}, x = \frac{3 - 13}{2}

Verify Solutions:

x = \frac{3 + 13}{2}

True

, x = \frac{3 - 13}{2}

False

The solution is

x = \frac{3 + 13}{2}

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

lo g_{10} (x) (9) = 2

2 lo g_{10} (x + 3) = 2 x + 3

lo g_{10} (x) + lo g_{10} (x + 4) = - 1

lo g_{125} (x) - lo g_{5} (x) = - 2

What is the answer to ln(x+1)-ln(x-2)=ln(x) ?
The answer to ln(x+1)-ln(x-2)=ln(x) is x=(3+sqrt(13))/2
Solve for x: ln(x+1)-ln(x-2)=ln(x)
The solution is x=(3+sqrt(13))/2