Mister Exam

Other calculators

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

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
log(x) - log(x - 1) = t
$$\log{\left(x \right)} - \log{\left(x - 1 \right)} = t$$
Simplify
The graph
Sum and product of roots [src] 
sum
    /    t  \     /    t  \
    |   e   |     |   e   |
I*im|-------| + re|-------|
    |      t|     |      t|
    \-1 + e /     \-1 + e /
$$\operatorname{re}{\left(\frac{e^{t}}{e^{t} - 1}\right)} + i \operatorname{im}{\left(\frac{e^{t}}{e^{t} - 1}\right)}$$ 
=
    /    t  \     /    t  \
    |   e   |     |   e   |
I*im|-------| + re|-------|
    |      t|     |      t|
    \-1 + e /     \-1 + e /
$$\operatorname{re}{\left(\frac{e^{t}}{e^{t} - 1}\right)} + i \operatorname{im}{\left(\frac{e^{t}}{e^{t} - 1}\right)}$$ 
product
    /    t  \     /    t  \
    |   e   |     |   e   |
I*im|-------| + re|-------|
    |      t|     |      t|
    \-1 + e /     \-1 + e /
$$\operatorname{re}{\left(\frac{e^{t}}{e^{t} - 1}\right)} + i \operatorname{im}{\left(\frac{e^{t}}{e^{t} - 1}\right)}$$ 
=
    /    t  \     /    t  \
    |   e   |     |   e   |
I*im|-------| + re|-------|
    |      t|     |      t|
    \-1 + e /     \-1 + e /
$$\operatorname{re}{\left(\frac{e^{t}}{e^{t} - 1}\right)} + i \operatorname{im}{\left(\frac{e^{t}}{e^{t} - 1}\right)}$$ 
i*im(exp(t)/(-1 + exp(t))) + re(exp(t)/(-1 + exp(t)))
Rapid solution [src] 
         /    t  \     /    t  \
         |   e   |     |   e   |
x1 = I*im|-------| + re|-------|
         |      t|     |      t|
         \-1 + e /     \-1 + e /
$$x_{1} = \operatorname{re}{\left(\frac{e^{t}}{e^{t} - 1}\right)} + i \operatorname{im}{\left(\frac{e^{t}}{e^{t} - 1}\right)}$$ 
x1 = re(exp(t)/(exp(t) - 1)) + i*im(exp(t)/(exp(t) - 1))
    © Mister Exam – Calculator