Sr Examen
-9^x+(8-9*x)*1/2^x=0 la ecuación
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Solución
Ha introducido
[src]
x -x - 9 + (8 - 9*x)*2 = 0
$$- 9^{x} + \left(\frac{1}{2}\right)^{x} \left(8 - 9 x\right) = 0$$
Suma y producto de raíces
[src]
suma
/ / 9 ________\\ / / / 9 ________\\\ / / / 9 ________\\\
| | \/ 559872 || | |/ 11 \ | \/ 559872 ||| | |/ 11 \ | \/ 559872 |||
| | ----------|| | || -- | | ----------||| | || -- | | ----------|||
| | 3 || log(11019960576) | ||9 ____ /pi\ 18 /pi\| | 3 ||| log(11019960576) | ||9 ____ /pi\ 18 /pi\| | 3 |||
- W\log\18 // + ---------------- - re|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /|| + ---------------- I*im|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /||
9 \ \\ \9 / \9 // // 9 \ \\ \9 / \9 // //
----------------------------------------- + ------------------------------------------------------------------------------- - ------------------------------------------------------------
log(18) log(18) log(18)
$$\frac{- W\left(\log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right) + \frac{\log{\left(11019960576 \right)}}{9}}{\log{\left(18 \right)}} + \left(\frac{- \operatorname{re}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)} + \frac{\log{\left(11019960576 \right)}}{9}}{\log{\left(18 \right)}} - \frac{i \operatorname{im}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)}}{\log{\left(18 \right)}}\right)$$
=
/ / 9 ________\\ / / / 9 ________\\\ / / / 9 ________\\\
| | \/ 559872 || | |/ 11 \ | \/ 559872 ||| | |/ 11 \ | \/ 559872 |||
| | ----------|| | || -- | | ----------||| | || -- | | ----------|||
| | 3 || log(11019960576) | ||9 ____ /pi\ 18 /pi\| | 3 ||| log(11019960576) | ||9 ____ /pi\ 18 /pi\| | 3 |||
- W\log\18 // + ---------------- - re|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /|| + ---------------- I*im|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /||
9 \ \\ \9 / \9 // // 9 \ \\ \9 / \9 // //
----------------------------------------- + ------------------------------------------------------------------------------- - ------------------------------------------------------------
log(18) log(18) log(18)
$$\frac{- W\left(\log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right) + \frac{\log{\left(11019960576 \right)}}{9}}{\log{\left(18 \right)}} + \frac{- \operatorname{re}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)} + \frac{\log{\left(11019960576 \right)}}{9}}{\log{\left(18 \right)}} - \frac{i \operatorname{im}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)}}{\log{\left(18 \right)}}$$
producto
/ / 9 ________\\ / / / / 9 ________\\\ / / / 9 ________\\\\
| | \/ 559872 || | | |/ 11 \ | \/ 559872 ||| | |/ 11 \ | \/ 559872 ||||
| | ----------|| | | || -- | | ----------||| | || -- | | ----------||||
| | 3 || log(11019960576) | | ||9 ____ /pi\ 18 /pi\| | 3 ||| log(11019960576) | ||9 ____ /pi\ 18 /pi\| | 3 ||||
- W\log\18 // + ---------------- |- re|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /|| + ---------------- I*im|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /|||
9 | \ \\ \9 / \9 // // 9 \ \\ \9 / \9 // //|
-----------------------------------------*|------------------------------------------------------------------------------- - ------------------------------------------------------------|
log(18) \ log(18) log(18) /
$$\frac{- W\left(\log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right) + \frac{\log{\left(11019960576 \right)}}{9}}{\log{\left(18 \right)}} \left(\frac{- \operatorname{re}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)} + \frac{\log{\left(11019960576 \right)}}{9}}{\log{\left(18 \right)}} - \frac{i \operatorname{im}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)}}{\log{\left(18 \right)}}\right)$$
=
/ / / 9 ________\\ \ / / / / 9 ________\\\ / / / 9 ________\\\ \
| | | \/ 559872 || | | | |/ 11 \ | \/ 559872 ||| | |/ 11 \ | \/ 559872 ||| |
| | | ----------|| | | | || -- | | ----------||| | || -- | | ----------||| |
| | | 3 || | | | ||9 ____ /pi\ 18 /pi\| | 3 ||| | ||9 ____ /pi\ 18 /pi\| | 3 ||| |
\- 9*W\log\18 // + log(11019960576)/*|- 9*re|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /|| - 9*I*im|W||\/ -1 *cos|--| - (-1) *sin|--||*log\18 /|| + log(11019960576)|
\ \ \\ \9 / \9 // // \ \\ \9 / \9 // // /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
81*log (18)
$$\frac{\left(- 9 W\left(\log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right) + \log{\left(11019960576 \right)}\right) \left(- 9 \operatorname{re}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)} + \log{\left(11019960576 \right)} - 9 i \operatorname{im}{\left(W\left(\left(- \left(-1\right)^{\frac{11}{18}} \sin{\left(\frac{\pi}{9} \right)} + \sqrt[9]{-1} \cos{\left(\frac{\pi}{9} \right)}\right) \log{\left(18^{\frac{\sqrt[9]{559872}}{3}} \right)}\right)\right)}\right)}{81 \log{\left(18 \right)}^{2}}$$
(-9*LambertW(log(18^(559872^(1/9)/3))) + log(11019960576))*(-9*re(LambertW(((-1)^(1/9)*cos(pi/9) - (-1)^(11/18)*sin(pi/9))*log(18^(559872^(1/9)/3)))) - 9*i*im(LambertW(((-1)^(1/9)*cos(pi/9) - (-1)^(11/18)*sin(pi/9))*log(18^(559872^(1/9)/3)))) + log(11019960576))/(81*log(18)^2)