What is the answer to ln(x+3)-ln(x-2)=ln(x) ?

The answer to ln(x+3)-ln(x-2)=ln(x) is x=(3+sqrt(21))/2

Solve for x: ln(x+3)-ln(x-2)=ln(x)

The solution is x=(3+sqrt(21))/2

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ln (x + 3) - ln (x - 2) = ln (x)

x = \frac{3 + 21}{2}

Decimal Notation

x = 3.79128 \dots

Solution steps

ln (x + 3) - ln (x - 2) = ln (x)

Add

ln (x - 2)

to both sides

ln (x + 3) - ln (x - 2) + ln (x - 2) = ln (x) + ln (x - 2)

Simplify

ln (x + 3) = ln (x) + ln (x - 2)

Apply log rules

x + 3 = x (x - 2)

Solve

x + 3 = x (x - 2) : x = \frac{3 + 21}{2}, x = \frac{3 - 21}{2}

x = \frac{3 + 21}{2}, x = \frac{3 - 21}{2}

Verify Solutions:

x = \frac{3 + 21}{2}

True

, x = \frac{3 - 21}{2}

False

The solution is

x = \frac{3 + 21}{2}

ln (x^{2} - x) = 1

x, 2 = - lo g_{10} (x)

- 1 - 5 \cdot ln (x) = 1

lo g_{2} (k + 2) - lo g_{2} (3 - k) = - 2

lo g_{2} (x) = 1 0^{6}

What is the answer to ln(x+3)-ln(x-2)=ln(x) ?
The answer to ln(x+3)-ln(x-2)=ln(x) is x=(3+sqrt(21))/2
Solve for x: ln(x+3)-ln(x-2)=ln(x)
The solution is x=(3+sqrt(21))/2