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

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

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solvefor x,ln(x)-ln(x-1)=1

solve for

x, 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}

x, ln (x) - ln (x - 1) = t

lo g_{a} (8) = 2

1 - x = ln (x)

ln (x) = 5.856401977

4 ln (7 x - 1) - 6 = 6

What is the answer to solvefor x,ln(x)-ln(x-1)=1 ?
The answer to solvefor x,ln(x)-ln(x-1)=1 is x= e/(e-1)