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

The answer to solvefor x,ln(x)-ln(x-1)=t is x=-(e^t)/(1-e^t) {No Solution}

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

solve for

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

x = - \frac{e ^{t}}{1 - e ^{t}} {No Solution}

Solution steps

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

Add

ln (x - 1)

to both sides

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

Simplify

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

Apply log rules

x = e^{t} (x - 1)

Solve

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

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

Verify Solutions:

x = - \frac{e ^{t}}{1 - e ^{t}} {No Solution}

The solution is

x = - \frac{e ^{t}}{1 - e ^{t}} {No Solution}

lo g_{a} (8) = 2

1 - x = ln (x)

ln (x) = 5.856401977

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

lo g_{10} (x) + lo g_{10} (x + 2) = 9

What is the answer to solvefor x,ln(x)-ln(x-1)=t ?
The answer to solvefor x,ln(x)-ln(x-1)=t is x=-(e^t)/(1-e^t) {No Solution}