What is the answer to ln(x+5)-ln(x-4)=ln(x) ?

The answer to ln(x+5)-ln(x-4)=ln(x) is x=(5+3sqrt(5))/2

Solve for x: ln(x+5)-ln(x-4)=ln(x)

The solution is x=(5+3sqrt(5))/2

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ln (x + 5) - ln (x - 4) = ln (x)

x = \frac{5 + 3 5}{2}

Solution steps

ln (x + 5) - ln (x - 4) = ln (x)

Add

ln (x - 4)

to both sides

ln (x + 5) - ln (x - 4) + ln (x - 4) = ln (x) + ln (x - 4)

Simplify

ln (x + 5) = ln (x) + ln (x - 4)

Apply log rules

x + 5 = x (x - 4)

Solve

x + 5 = x (x - 4) : x = \frac{5 + 3 5}{2}, x = \frac{5 - 3 5}{2}

x = \frac{5 + 3 5}{2}, x = \frac{5 - 3 5}{2}

Verify Solutions:

x = \frac{5 + 3 5}{2}

True

, x = \frac{5 - 3 5}{2}

False

The solution is

x = \frac{5 + 3 5}{2}

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

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

1.85 = - lo g_{10} (x)

lo g_{x} (0.1) = - \frac{1}{3}

10 lo g_{10} (x) = 26.5

What is the answer to ln(x+5)-ln(x-4)=ln(x) ?
The answer to ln(x+5)-ln(x-4)=ln(x) is x=(5+3sqrt(5))/2
Solve for x: ln(x+5)-ln(x-4)=ln(x)
The solution is x=(5+3sqrt(5))/2