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Identical expressions
- log two ^2x-log2x-2= zero
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- logarithm of two squared x minus logarithm of 2x minus 2 equally zero
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Similar expressions
- log2^2x+log2x-2=0
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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)