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

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

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

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

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

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

Decimal

x = 1.15651 \dots

Solution steps

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

Add

ln (x - 1)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

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

Verify Solutions:

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

True

The solution is

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

lo g_{2} (3 x - 4) = lo g_{2} (5)

5.75 = - lo g_{10} (x)

lo g_{10} (0.3 x + 1.8) = 4

ln (x) = 4.9

lo g_{12} (5 x + 7) = lo g_{12} (22)

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