Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2=5
-
Equation k^2+k=0
-
Equation 5x=0
-
Equation x^2-15=2x
- Express {x} in terms of y where:
- -4*x+3*y=9
- -2*x-19*y=-11
- -5*x+15*y=-15
- -1*x+7*y=-11
-
Identical expressions
- a^x-b*x= zero
- a to the power of x minus b multiply by x equally 0
- a to the power of x minus b multiply by x equally zero
- ax-b*x=0
- a^x-bx=0
- ax-bx=0
- a^x-b*x=O
-
Similar expressions
- a^x+b*x=0
a^x-b*x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
The graph
Sum and product of roots
[src]
sum
/ /-log(a) \\ / /-log(a) \\
|W|--------|| |W|--------||
| \ b /| | \ b /|
- re|-----------| - I*im|-----------|
\ log(a) / \ log(a) /
$$- \operatorname{re}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)} - i \operatorname{im}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)}$$
=
/ /-log(a) \\ / /-log(a) \\
|W|--------|| |W|--------||
| \ b /| | \ b /|
- re|-----------| - I*im|-----------|
\ log(a) / \ log(a) /
$$- \operatorname{re}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)} - i \operatorname{im}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)}$$
product
/ /-log(a) \\ / /-log(a) \\
|W|--------|| |W|--------||
| \ b /| | \ b /|
- re|-----------| - I*im|-----------|
\ log(a) / \ log(a) /
$$- \operatorname{re}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)} - i \operatorname{im}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)}$$
=
/ /-log(a) \\ / /-log(a) \\
|W|--------|| |W|--------||
| \ b /| | \ b /|
- re|-----------| - I*im|-----------|
\ log(a) / \ log(a) /
$$- \operatorname{re}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)} - i \operatorname{im}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)}$$
-re(LambertW(-log(a)/b)/log(a)) - i*im(LambertW(-log(a)/b)/log(a))
Rapid solution
[src]
/ /-log(a) \\ / /-log(a) \\
|W|--------|| |W|--------||
| \ b /| | \ b /|
x1 = - re|-----------| - I*im|-----------|
\ log(a) / \ log(a) /
$$x_{1} = - \operatorname{re}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)} - i \operatorname{im}{\left(\frac{W\left(- \frac{\log{\left(a \right)}}{b}\right)}{\log{\left(a \right)}}\right)}$$
x1 = -re(LambertW(-log(a)/b)/log(a)) - i*im(LambertW(-log(a)/b)/log(a))