Sr Examen
log2/2(x)−5⋅log2(x)+4=0. la ecuación
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Solución
Ha introducido
[src]
log(2) log(x) ------*x - 5*------ + 4 = 0 2 log(2)
$$\left(x \frac{\log{\left(2 \right)}}{2} - 5 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right) + 4 = 0$$
Respuesta rápida
[src]
/ 4/5 2 \
|-2 *log (2) |
-10*W|--------------, -1|
\ 10 /
x1 = -------------------------
2
log (2)
$$x_{1} = - \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}}$$
41 21 256 34
-- --- --- ---
46 598 299 299
2 *3 *5 *7
x2 = ------------------
5
$$x_{2} = \frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5}$$
x2 = 2^(41/46)*3^(21/598)*5^(256/299)*7^(34/299)/5
Suma y producto de raíces
[src]
suma
/ 4/5 2 \ 41 21 256 34
|-2 *log (2) | -- --- --- ---
10*W|--------------, -1| 46 598 299 299
\ 10 / 2 *3 *5 *7
- ------------------------ + ------------------
2 5
log (2)
$$\frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5} - \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}}$$
=
/ 4/5 2 \ 41 21 256 34
|-2 *log (2) | -- --- --- ---
10*W|--------------, -1| 46 598 299 299
\ 10 / 2 *3 *5 *7
- ------------------------ + ------------------
2 5
log (2)
$$\frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5} - \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}}$$
producto
/ 4/5 2 \ 41 21 256 34
|-2 *log (2) | -- --- --- ---
-10*W|--------------, -1| 46 598 299 299
\ 10 / 2 *3 *5 *7
-------------------------*------------------
2 5
log (2)
$$- \frac{10 W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}} \frac{2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}}}{5}$$
=
41 21 256 34
-- --- --- --- / 4/5 2 \
46 598 299 299 |-2 *log (2) |
-2*2 *3 *5 *7 *W|--------------, -1|
\ 10 /
-------------------------------------------
2
log (2)
$$- \frac{2 \cdot 2^{\frac{41}{46}} \cdot 3^{\frac{21}{598}} \cdot 5^{\frac{256}{299}} \cdot 7^{\frac{34}{299}} W_{-1}\left(- \frac{2^{\frac{4}{5}} \log{\left(2 \right)}^{2}}{10}\right)}{\log{\left(2 \right)}^{2}}$$
-2*2^(41/46)*3^(21/598)*5^(256/299)*7^(34/299)*LambertW(-2^(4/5)*log(2)^2/10, -1)/log(2)^2