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

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

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

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

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

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

Solution steps

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

Add

ln (x - 1)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

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

Verify Solutions:

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

True

The solution is

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

lo g_{10} (x - 15) + lo g_{10} (x) = 2

3 lo g_{8} (3) = lo g_{8} (x)

lo g_{10} (x) = 4.3

lo g_{3} (2 x^{2} + 17 x) = 2

lo g_{10} (y + 21) + lo g_{10} (y) = 2

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