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

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

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

The solution is x=(2e+sqrt(e)-1)/(e-1)

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ln (x - 1) - ln (x - 2) = \frac{1}{2}

x = \frac{2 e + e - 1}{e - 1}

Decimal Notation

x = 3.54149 \dots

Solution steps

ln (x - 1) - ln (x - 2) = \frac{1}{2}

Add

ln (x - 2)

to both sides

ln (x - 1) - ln (x - 2) + ln (x - 2) = \frac{1}{2} + ln (x - 2)

Simplify

ln (x - 1) = \frac{1}{2} + ln (x - 2)

Apply log rules

x - 1 = e (x - 2)

Solve

x - 1 = e (x - 2) : x = \frac{2 e + e - 1}{e - 1}

x = \frac{2 e + e - 1}{e - 1}

Verify Solutions:

x = \frac{2 e + e - 1}{e - 1}

True

The solution is

x = \frac{2 e + e - 1}{e - 1}

ln (x + 8) + ln (x - 5) = 2 ln (x)

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

e^{3 l n (x)} = x^{3}

lo g_{5} (x + 5) - lo g_{5} (x - 1) = 2

lo g_{10} (x + 3) - lo g_{10} (x) = 1

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