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Otras calculadoras
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- La ecuación:
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Ecuación (x+9)^2=36*x
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Ecuación a+120=2000/5
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Ecuación (|x|)=6
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Ecuación 6*x=12
- Expresar {x} en función de y en la ecuación:
- -6*x-12*y=9
- 9*x-1*y=17
- 10*x-2*y=11
- 12*x-3*y=-2
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Expresiones idénticas
- lg^ dos (100x)+lg^ dos (10x)=14lg(x)+ quince
- lg al cuadrado (100x) más lg al cuadrado (10x) es igual a 14lg(x) más 15
- lg en el grado dos (100x) más lg en el grado dos (10x) es igual a 14lg(x) más quince
- lg2(100x)+lg2(10x)=14lg(x)+15
- lg2100x+lg210x=14lgx+15
- lg²(100x)+lg²(10x)=14lg(x)+15
- lg en el grado 2(100x)+lg en el grado 2(10x)=14lg(x)+15
- lg^2100x+lg^210x=14lgx+15
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Expresiones semejantes
- lg^2(100x)+lg^2(10x)=14lg(x)-15
- lg^2(100x)-lg^2(10x)=14lg(x)+15
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Expresiones con funciones
- lg
- lg(x)=0.68167
- lg(x/(x-75,33))=0,459
- lg(0,525:x)=0,25
- lg(x^2+9*x)=1
- lg(d/1000)⋅lg(d)=28
- lg
- lg(x)=0.68167
- lg(x/(x-75,33))=0,459
- lg(0,525:x)=0,25
- lg(x^2+9*x)=1
- lg(d/1000)⋅lg(d)=28
lg^2(100x)+lg^2(10x)=14lg(x)+15 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 log (100*x) + log (10*x) = 14*log(x) + 15
$$\log{\left(10 x \right)}^{2} + \log{\left(100 x \right)}^{2} = 14 \log{\left(x \right)} + 15$$
Suma y producto de raíces
[src]
suma
/ _____________________________\ / _____________________________\ / _____________________________\ / _____________________________\
| / 2 | | / 2 | | / 2 | | / 2 |
____ |\/ -79 + log (10) + 42*log(10) | 7/2 ____ 7/2 |\/ -79 + log (10) + 42*log(10) | ____ |\/ -79 + log (10) + 42*log(10) | 7/2 ____ 7/2 |\/ -79 + log (10) + 42*log(10) |
\/ 10 *cos|--------------------------------|*e I*\/ 10 *e *sin|--------------------------------| \/ 10 *cos|--------------------------------|*e I*\/ 10 *e *sin|--------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
------------------------------------------------- - --------------------------------------------------- + ------------------------------------------------- + ---------------------------------------------------
100 100 100 100
$$\left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} - \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right) + \left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} + \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right)$$
=
/ _____________________________\
| / 2 |
____ |\/ -79 + log (10) + 42*log(10) | 7/2
\/ 10 *cos|--------------------------------|*e
\ 2 /
-------------------------------------------------
50
$$\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{50}$$
producto
/ / _____________________________\ / _____________________________\\ / / _____________________________\ / _____________________________\\ | | / 2 | | / 2 || | | / 2 | | / 2 || | ____ |\/ -79 + log (10) + 42*log(10) | 7/2 ____ 7/2 |\/ -79 + log (10) + 42*log(10) || | ____ |\/ -79 + log (10) + 42*log(10) | 7/2 ____ 7/2 |\/ -79 + log (10) + 42*log(10) || |\/ 10 *cos|--------------------------------|*e I*\/ 10 *e *sin|--------------------------------|| |\/ 10 *cos|--------------------------------|*e I*\/ 10 *e *sin|--------------------------------|| | \ 2 / \ 2 /| | \ 2 / \ 2 /| |------------------------------------------------- - ---------------------------------------------------|*|------------------------------------------------- + ---------------------------------------------------| \ 100 100 / \ 100 100 /
$$\left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} - \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right) \left(\frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} + \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}\right)$$
=
7 e ---- 1000
$$\frac{e^{7}}{1000}$$
exp(7)/1000
Respuesta rápida
[src]
/ _____________________________\ / _____________________________\
| / 2 | | / 2 |
____ |\/ -79 + log (10) + 42*log(10) | 7/2 ____ 7/2 |\/ -79 + log (10) + 42*log(10) |
\/ 10 *cos|--------------------------------|*e I*\/ 10 *e *sin|--------------------------------|
\ 2 / \ 2 /
x1 = ------------------------------------------------- - ---------------------------------------------------
100 100
$$x_{1} = \frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} - \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}$$
/ _____________________________\ / _____________________________\
| / 2 | | / 2 |
____ |\/ -79 + log (10) + 42*log(10) | 7/2 ____ 7/2 |\/ -79 + log (10) + 42*log(10) |
\/ 10 *cos|--------------------------------|*e I*\/ 10 *e *sin|--------------------------------|
\ 2 / \ 2 /
x2 = ------------------------------------------------- + ---------------------------------------------------
100 100
$$x_{2} = \frac{\sqrt{10} e^{\frac{7}{2}} \cos{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100} + \frac{\sqrt{10} i e^{\frac{7}{2}} \sin{\left(\frac{\sqrt{-79 + \log{\left(10 \right)}^{2} + 42 \log{\left(10 \right)}}}{2} \right)}}{100}$$
x2 = sqrt(10)*exp(7/2)*cos(sqrt(-79 + log(10)^2 + 42*log(10))/2)/100 + sqrt(10)*i*exp(7/2)*sin(sqrt(-79 + log(10)^2 + 42*log(10))/2)/100
Respuesta numérica
[src]
x1 = -0.771111469526577 + 0.708533880624647*i
x2 = -0.771111469526577 - 0.708533880624647*i
x2 = -0.771111469526577 - 0.708533880624647*i