Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación (x-3)*(x+2)=0
-
Ecuación z^2-6*z+10=0
-
Ecuación 9x−9(x+1)=−2x
-
Ecuación 4/(x-4)=-5
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- 9*x+10*y=5
-
Expresiones idénticas
- ln(x)* diez ^ seis =(ln(n))^y
- ln(x) multiplicar por 10 en el grado 6 es igual a (ln(n)) en el grado y
- ln(x) multiplicar por diez en el grado seis es igual a (ln(n)) en el grado y
- ln(x)*106=(ln(n))y
- lnx*106=lnny
- ln(x)*10⁶=(ln(n))^y
- ln(x)10^6=(ln(n))^y
- ln(x)106=(ln(n))y
- lnx106=lnny
- lnx10^6=lnn^y
-
Expresiones con funciones
- ln
- ln(101,3/x)=17,47/8,314*(1/268,15-1/192,15)
- ln((2x)/(x-4))-x=0
- ln(x)=13
- ln2*e^x=0
- ln(x/0,34)=22282,49539
- ln
- ln(101,3/x)=17,47/8,314*(1/268,15-1/192,15)
- ln((2x)/(x-4))-x=0
- ln(x)=13
- ln2*e^x=0
- ln(x/0,34)=22282,49539
ln(x)*10^6=(ln(n))^y la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
y log(x)*1000000 = log (n)
$$1000000 \log{\left(x \right)} = \log{\left(n \right)}^{y}$$
Solución detallada
Tenemos la ecuación:
$$1000000 \log{\left(x \right)} = \log{\left(n \right)}^{y}$$
o
$$- \log{\left(n \right)}^{y} + 1000000 \log{\left(x \right)} = 0$$
o
$$- \log{\left(n \right)}^{y} = - 1000000 \log{\left(x \right)}$$
o
$$\log{\left(n \right)}^{y} = 1000000 \log{\left(x \right)}$$
- es la ecuación exponencial más simple
Sustituimos
$$v = \log{\left(n \right)}^{y}$$
obtendremos
$$v - 1000000 \log{\left(x \right)} = 0$$
o
$$v - 1000000 \log{\left(x \right)} = 0$$
hacemos cambio inverso
$$\log{\left(n \right)}^{y} = v$$
o
$$y = \frac{\log{\left(v \right)}}{\log{\left(\log{\left(n \right)} \right)}}$$
Entonces la respuesta definitiva es
$$y_{1} = \frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}} = \frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}$$
$$1000000 \log{\left(x \right)} = \log{\left(n \right)}^{y}$$
o
$$- \log{\left(n \right)}^{y} + 1000000 \log{\left(x \right)} = 0$$
o
$$- \log{\left(n \right)}^{y} = - 1000000 \log{\left(x \right)}$$
o
$$\log{\left(n \right)}^{y} = 1000000 \log{\left(x \right)}$$
- es la ecuación exponencial más simple
Sustituimos
$$v = \log{\left(n \right)}^{y}$$
obtendremos
$$v - 1000000 \log{\left(x \right)} = 0$$
o
$$v - 1000000 \log{\left(x \right)} = 0$$
hacemos cambio inverso
$$\log{\left(n \right)}^{y} = v$$
o
$$y = \frac{\log{\left(v \right)}}{\log{\left(\log{\left(n \right)} \right)}}$$
Entonces la respuesta definitiva es
$$y_{1} = \frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}} = \frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}$$
Gráfica
Suma y producto de raíces
[src]
suma
/log(1000000*log(x))\ /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
\ log(log(n)) / \ log(log(n)) /
$$\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)}$$
=
/log(1000000*log(x))\ /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
\ log(log(n)) / \ log(log(n)) /
$$\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)}$$
producto
/log(1000000*log(x))\ /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
\ log(log(n)) / \ log(log(n)) /
$$\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)}$$
=
/log(1000000*log(x))\ /log(1000000*log(x))\
I*im|-------------------| + re|-------------------|
\ log(log(n)) / \ log(log(n)) /
$$\operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)}$$
i*im(log(1000000*log(x))/log(log(n))) + re(log(1000000*log(x))/log(log(n)))
Respuesta rápida
[src]
/log(1000000*log(x))\ /log(1000000*log(x))\
y1 = I*im|-------------------| + re|-------------------|
\ log(log(n)) / \ log(log(n)) /
$$y_{1} = \operatorname{re}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)} + i \operatorname{im}{\left(\frac{\log{\left(1000000 \log{\left(x \right)} \right)}}{\log{\left(\log{\left(n \right)} \right)}}\right)}$$
y1 = re(log(1000000*log(x))/log(log(n))) + i*im(log(1000000*log(x))/log(log(n)))