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Ecuación 8*x-3*(2*x+1)=2*x+4
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Ecuación 2*x^2+6*x+9=
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Expresiones idénticas
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- 3log4^2-7log4^x+2=0
- 3log(4)^2-7*log(4)^x+2=O
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Expresiones semejantes
- 3log(4)^2+7*log(4)^x+2=0
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Expresiones con funciones
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3log(4)^2-7*log(4)^x+2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 x 3*log (4) - 7*log (4) + 2 = 0
$$\left(- 7 \log{\left(4 \right)}^{x} + 3 \log{\left(4 \right)}^{2}\right) + 2 = 0$$
Solución detallada
Tenemos la ecuación:
$$\left(- 7 \log{\left(4 \right)}^{x} + 3 \log{\left(4 \right)}^{2}\right) + 2 = 0$$
o
$$\left(- 7 \log{\left(4 \right)}^{x} + 3 \log{\left(4 \right)}^{2}\right) + 2 = 0$$
Sustituimos
$$v = 1$$
obtendremos
$$- 7 \log{\left(4 \right)}^{x} + 2 + 3 \log{\left(4 \right)}^{2} = 0$$
o
$$- 7 \log{\left(4 \right)}^{x} + 2 + 3 \log{\left(4 \right)}^{2} = 0$$
hacemos cambio inverso
$$1 = v$$
o
$$x = \tilde{\infty} \log{\left(v \right)}$$
Entonces la respuesta definitiva es
$$x_{1} = \frac{\log{\left(\log{\left(\left(\frac{2}{7} + \frac{3 \log{\left(4 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)} \right)}}{\log{\left(1 \right)}} = \tilde{\infty}$$
$$\left(- 7 \log{\left(4 \right)}^{x} + 3 \log{\left(4 \right)}^{2}\right) + 2 = 0$$
o
$$\left(- 7 \log{\left(4 \right)}^{x} + 3 \log{\left(4 \right)}^{2}\right) + 2 = 0$$
Sustituimos
$$v = 1$$
obtendremos
$$- 7 \log{\left(4 \right)}^{x} + 2 + 3 \log{\left(4 \right)}^{2} = 0$$
o
$$- 7 \log{\left(4 \right)}^{x} + 2 + 3 \log{\left(4 \right)}^{2} = 0$$
hacemos cambio inverso
$$1 = v$$
o
$$x = \tilde{\infty} \log{\left(v \right)}$$
Entonces la respuesta definitiva es
$$x_{1} = \frac{\log{\left(\log{\left(\left(\frac{2}{7} + \frac{3 \log{\left(4 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)} \right)}}{\log{\left(1 \right)}} = \tilde{\infty}$$
Suma y producto de raíces
[src]
suma
/ 1 \ / 1 \ | -----------| | -----------| | log(log(4))| | log(log(4))| |/ 2 \ | |/ 2 \ | ||2 12*log (2)| | ||2 3*log (4)| | log||- + ----------| | + log||- + ---------| | \\7 7 / / \\7 7 / /
$$\log{\left(\left(\frac{2}{7} + \frac{12 \log{\left(2 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)} + \log{\left(\left(\frac{2}{7} + \frac{3 \log{\left(4 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)}$$
=
/ 1 \ / 1 \ | -----------| | -----------| | log(log(4))| | log(log(4))| |/ 2 \ | |/ 2 \ | ||2 3*log (4)| | ||2 12*log (2)| | log||- + ---------| | + log||- + ----------| | \\7 7 / / \\7 7 / /
$$\log{\left(\left(\frac{2}{7} + \frac{3 \log{\left(4 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)} + \log{\left(\left(\frac{2}{7} + \frac{12 \log{\left(2 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)}$$
producto
/ 1 \ / 1 \ | -----------| | -----------| | log(log(4))| | log(log(4))| |/ 2 \ | |/ 2 \ | ||2 12*log (2)| | ||2 3*log (4)| | log||- + ----------| |*log||- + ---------| | \\7 7 / / \\7 7 / /
$$\log{\left(\left(\frac{2}{7} + \frac{12 \log{\left(2 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)} \log{\left(\left(\frac{2}{7} + \frac{3 \log{\left(4 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)}$$
=
/ / 1 \\ | | -1 -----------|| | | ----------- log(log(4))|| | | log(log(4)) / 2 \ || | log\7 *\2 + 3*log (4)/ /| | --------------------------------------------| | log(2) + log(log(2)) | |/ 2 \ | ||2 12*log (2)| | log||- + ----------| | \\7 7 / /
$$\log{\left(\left(\frac{2}{7} + \frac{12 \log{\left(2 \right)}^{2}}{7}\right)^{\frac{\log{\left(\frac{\left(2 + 3 \log{\left(4 \right)}^{2}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}}}{7^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}}} \right)}}{\log{\left(\log{\left(2 \right)} \right)} + \log{\left(2 \right)}}} \right)}$$
log((2/7 + 12*log(2)^2/7)^(log(7^(-1/log(log(4)))*(2 + 3*log(4)^2)^(1/log(log(4))))/(log(2) + log(log(2)))))
Respuesta rápida
[src]
/ 1 \
| -----------|
| log(log(4))|
|/ 2 \ |
||2 12*log (2)| |
x1 = log||- + ----------| |
\\7 7 / /
$$x_{1} = \log{\left(\left(\frac{2}{7} + \frac{12 \log{\left(2 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)}$$
/ 1 \
| -----------|
| log(log(4))|
|/ 2 \ |
||2 3*log (4)| |
x2 = log||- + ---------| |
\\7 7 / /
$$x_{2} = \log{\left(\left(\frac{2}{7} + \frac{3 \log{\left(4 \right)}^{2}}{7}\right)^{\frac{1}{\log{\left(\log{\left(4 \right)} \right)}}} \right)}$$
x2 = log((2/7 + 3*log(4)^2/7)^(1/log(log(4))))