What is the answer to ln(x-3)-ln(x-5)=ln(5) ?

The answer to ln(x-3)-ln(x-5)=ln(5) is x= 11/2

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ln(x-3)-ln(x-5)=ln(5)

ln (x - 3) - ln (x - 5) = ln (5)

x = \frac{11}{2}

Decimal Notation

x = 5.5

Solution steps

ln (x - 3) - ln (x - 5) = ln (5)

Add

ln (x - 5)

to both sides

ln (x - 3) - ln (x - 5) + ln (x - 5) = ln (5) + ln (x - 5)

Simplify

ln (x - 3) = ln (5) + ln (x - 5)

Apply log rules

x - 3 = 5 (x - 5)

Solve

x - 3 = 5 (x - 5) : x = \frac{11}{2}

x = \frac{11}{2}

Verify Solutions:

x = \frac{11}{2}

True

The solution is

x = \frac{11}{2}

ln (x) + 2 = 0

lo g_{2 x + 3} (81) = 2

ln (2 x - 3) - ln (x + 1) = e

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

lo g_{8} (3 x + 1) + 16 = 18

What is the answer to ln(x-3)-ln(x-5)=ln(5) ?
The answer to ln(x-3)-ln(x-5)=ln(5) is x= 11/2
Solve for x: ln(x-3)-ln(x-5)=ln(5)
The solution is x= 11/2