sqrt(3-5^x)*(2*(5^x)+8*(5^-x)-17)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
0 5 -15 -10 -5 10 15 500000000 -250000000
Suma y producto de raíces
[src]
log(2) 3*log(2) log(3)
- ------ + -------- + ------
log(5) log(5) log(5)
log ( 3 ) log ( 5 ) + ( − log ( 2 ) log ( 5 ) + 3 log ( 2 ) log ( 5 ) ) \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}} + \left(- \frac{\log{\left(2 \right)}}{\log{\left(5 \right)}} + \frac{3 \log{\left(2 \right)}}{\log{\left(5 \right)}}\right) log ( 5 ) log ( 3 ) + ( − log ( 5 ) log ( 2 ) + log ( 5 ) 3 log ( 2 ) )
log(3) 2*log(2)
------ + --------
log(5) log(5)
log ( 3 ) log ( 5 ) + 2 log ( 2 ) log ( 5 ) \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}} + \frac{2 \log{\left(2 \right)}}{\log{\left(5 \right)}} log ( 5 ) log ( 3 ) + log ( 5 ) 2 log ( 2 )
-log(2) 3*log(2) log(3)
--------*--------*------
log(5) log(5) log(5)
− log ( 2 ) log ( 5 ) 3 log ( 2 ) log ( 5 ) log ( 3 ) log ( 5 ) - \frac{\log{\left(2 \right)}}{\log{\left(5 \right)}} \frac{3 \log{\left(2 \right)}}{\log{\left(5 \right)}} \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}} − log ( 5 ) log ( 2 ) log ( 5 ) 3 log ( 2 ) log ( 5 ) log ( 3 )
2
-3*log (2)*log(3)
-----------------
3
log (5)
− 3 log ( 2 ) 2 log ( 3 ) log ( 5 ) 3 - \frac{3 \log{\left(2 \right)}^{2} \log{\left(3 \right)}}{\log{\left(5 \right)}^{3}} − log ( 5 ) 3 3 log ( 2 ) 2 log ( 3 )
-3*log(2)^2*log(3)/log(5)^3
-log(2)
x1 = --------
log(5)
x 1 = − log ( 2 ) log ( 5 ) x_{1} = - \frac{\log{\left(2 \right)}}{\log{\left(5 \right)}} x 1 = − log ( 5 ) log ( 2 )
3*log(2)
x2 = --------
log(5)
x 2 = 3 log ( 2 ) log ( 5 ) x_{2} = \frac{3 \log{\left(2 \right)}}{\log{\left(5 \right)}} x 2 = log ( 5 ) 3 log ( 2 )
log(3)
x3 = ------
log(5)
x 3 = log ( 3 ) log ( 5 ) x_{3} = \frac{\log{\left(3 \right)}}{\log{\left(5 \right)}} x 3 = log ( 5 ) log ( 3 )