Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=0
-
Equation z^3=1
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Equation x^2-20=x
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Equation 4^x+3=11^x
- Express {x} in terms of y where:
- 3*x-7*y=-5
- -17*x-2*y=7
- -20*x-12*y=13
- -8*x+2*y=11
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Identical expressions
- two *x-ln(x)+ zero , five = zero
- 2 multiply by x minus ln(x) plus 0,5 equally 0
- two multiply by x minus ln(x) plus zero , five equally zero
- 2x-ln(x)+0,5=0
- 2x-lnx+0,5=0
- 2*x-ln(x)+0,5=O
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Similar expressions
- 2*x-ln(x)-0,5=0
- 2*x+ln(x)+0,5=0
2*x-ln(x)+0,5=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2*x - log(x) + 1/2 = 0
$$\left(2 x - \log{\left(x \right)}\right) + \frac{1}{2} = 0$$
Rapid solution
[src]
/ / 1/2\\ / / 1/2\\
re\W\-2*e // I*im\W\-2*e //
x1 = - -------------- - ----------------
2 2
$$x_{1} = - \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
x1 = -re(LambertW(-2*exp(1/2)))/2 - i*im(LambertW(-2*exp(1/2)))/2
Sum and product of roots
[src]
sum
/ / 1/2\\ / / 1/2\\
re\W\-2*e // I*im\W\-2*e //
- -------------- - ----------------
2 2
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
=
/ / 1/2\\ / / 1/2\\
re\W\-2*e // I*im\W\-2*e //
- -------------- - ----------------
2 2
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
product
/ / 1/2\\ / / 1/2\\
re\W\-2*e // I*im\W\-2*e //
- -------------- - ----------------
2 2
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
=
/ / 1/2\\ / / 1/2\\
re\W\-2*e // I*im\W\-2*e //
- -------------- - ----------------
2 2
$$- \frac{\operatorname{re}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2} - \frac{i \operatorname{im}{\left(W\left(- 2 e^{\frac{1}{2}}\right)\right)}}{2}$$
-re(LambertW(-2*exp(1/2)))/2 - i*im(LambertW(-2*exp(1/2)))/2
Numerical answer
[src]
x1 = -0.268160645457627 + 0.9262953167672*i
x1 = -0.268160645457627 + 0.9262953167672*i