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

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

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

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

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

Decimal Notation

x = 1.58197 \dots

Solution steps

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

Add

ln (x - 1)

to both sides

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

Simplify

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

Apply log rules

x = e (x - 1)

Solve

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

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

Verify Solutions:

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

True

The solution is

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

ln (x) - ln (3) = 2

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

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

lo g_{b} (125) = 3

ln (x) - \frac{3}{ln ( x )} = - 2

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