-9^x+(8-9*x)*1/2^x=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
Suma y producto de raíces
[src]
/ / 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)
log(18)−W(log(1839559872))+9log(11019960576)+log(18)−re(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872)))+9log(11019960576)−log(18)iim(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872)))
/ / 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)
log(18)−W(log(1839559872))+9log(11019960576)+log(18)−re(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872)))+9log(11019960576)−log(18)iim(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872)))
/ / 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) /
log(18)−W(log(1839559872))+9log(11019960576)log(18)−re(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872)))+9log(11019960576)−log(18)iim(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872)))
/ / / 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)
81log(18)2(−9W(log(1839559872))+log(11019960576))(−9re(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872)))+log(11019960576)−9iim(W((−(−1)1811sin(9π)+9−1cos(9π))log(1839559872))))
(-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)