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

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

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

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

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

Decimal Notation

x = 2.74593 \dots

Solution steps

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

Add

ln (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 2 = e (x - 1)

Solve

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

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

Verify Solutions:

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

True

The solution is

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

lo g_{10} (x) = 4.8

86.89 = 20 ln (x) + x

lo g_{10} (x) = 4.5

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

lo g_{10} (x) = - 1.9852

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