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

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

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

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

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

Decimal Notation

x = 0.58197 \dots

Solution steps

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

Add

ln (x)

to both sides

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

Simplify

ln (x + 1) = 1 + ln (x)

Apply log rules

x + 1 = e x

Solve

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

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

Verify Solutions:

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

True

The solution is

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

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

lo g_{3} (2 x + 1) = 2 + lo g_{3} (x - 9)

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

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

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

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