Mister Exam
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How to use it?
- Equation:
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Equation (5x+8)-(8x+14)=9
-
Equation cos(x)-1/2=0
-
Equation tg(x)=-1
-
Equation sin(x)=3/2
- Express {x} in terms of y where:
- 1*x+19*y=-10
- -16*x-7*y=-5
- -2*x+1*y=-8
- 1*x-19*y=-10
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Identical expressions
- log two ^2x-log2x-2= zero
- logarithm of 2 squared x minus logarithm of 2x minus 2 equally 0
- logarithm of two squared x minus logarithm of 2x minus 2 equally zero
- log22x-log2x-2=0
- log2²x-log2x-2=0
- log2 to the power of 2x-log2x-2=0
- log2^2x-log2x-2=O
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Similar expressions
- log2^2x+log2x-2=0
- log2^2x-log2x+2=0
log2^2x-log2x-2=0 equation
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The solution
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[src]
2 log (2)*x - log(2*x) - 2 = 0
$$\left(x \log{\left(2 \right)}^{2} - \log{\left(2 x \right)}\right) - 2 = 0$$
Sum and product of roots
[src]
sum
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
W|-------------| W|-------------, -1|
\ 2 / \ 2 /
- ---------------- - --------------------
2 2
log (2) log (2)
$$- \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} - \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}}$$
=
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
W|-------------| W|-------------, -1|
\ 2 / \ 2 /
- ---------------- - --------------------
2 2
log (2) log (2)
$$- \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} - \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}}$$
product
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
-W|-------------| -W|-------------, -1|
\ 2 / \ 2 /
------------------*----------------------
2 2
log (2) log (2)
$$- \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}} \left(- \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}}\right)$$
=
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
W|-------------|*W|-------------, -1|
\ 2 / \ 2 /
-------------------------------------
4
log (2)
$$\frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right) W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{4}}$$
LambertW(-log(2)^2*exp(-2)/2)*LambertW(-log(2)^2*exp(-2)/2, -1)/log(2)^4
Rapid solution
[src]
/ 2 -2 \
|-log (2)*e |
-W|-------------|
\ 2 /
x1 = ------------------
2
log (2)
$$x_{1} = - \frac{W\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}}$$
/ 2 -2 \
|-log (2)*e |
-W|-------------, -1|
\ 2 /
x2 = ----------------------
2
log (2)
$$x_{2} = - \frac{W_{-1}\left(- \frac{\log{\left(2 \right)}^{2}}{2 e^{2}}\right)}{\log{\left(2 \right)}^{2}}$$
x2 = -LambertW(-exp(-2)*log(2^2/2, -1)/log(2)^2)