Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x^2+6*x-7=0
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Equation ((46/5)-x)*(16/5)=16
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Equation -7-x=3x+17
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Equation -x^3+4*x^2+4*x-16=0
- Express {x} in terms of y where:
- 2*x+12*y=11
- -16*x-2*y=1
- 8*x+2*y=-12
- 15*x+11*y=14
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Identical expressions
- lg^ two (x)-lg^ two (10x)= six -lg^ two (100x)
- lg squared (x) minus lg squared (10x) equally 6 minus lg squared (100x)
- lg to the power of two (x) minus lg to the power of two (10x) equally six minus lg to the power of two (100x)
- lg2(x)-lg2(10x)=6-lg2(100x)
- lg2x-lg210x=6-lg2100x
- lg²(x)-lg²(10x)=6-lg²(100x)
- lg to the power of 2(x)-lg to the power of 2(10x)=6-lg to the power of 2(100x)
- lg^2x-lg^210x=6-lg^2100x
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Similar expressions
- lg^2(x)-lg^2(10x)=6+lg^2(100x)
- lg^2(x)+lg^2(10x)=6-lg^2(100x)
lg^2(x)-lg^2(10x)=6-lg^2(100x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2 2 log (x) - log (10*x) = 6 - log (100*x)
$$\log{\left(x \right)}^{2} - \log{\left(10 x \right)}^{2} = 6 - \log{\left(100 x \right)}^{2}$$
Rapid solution
[src]
/ _______________\ / _______________\
| ___ / 2 | | ___ / 2 |
cos\\/ 2 *\/ -3 + log (10) / I*sin\\/ 2 *\/ -3 + log (10) /
x1 = ----------------------------- - -------------------------------
10 10
$$x_{1} = \frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} - \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}$$
/ _______________\ / _______________\
| ___ / 2 | | ___ / 2 |
cos\\/ 2 *\/ -3 + log (10) / I*sin\\/ 2 *\/ -3 + log (10) /
x2 = ----------------------------- + -------------------------------
10 10
$$x_{2} = \frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} + \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}$$
x2 = cos(sqrt(2)*sqrt(-3 + log(10)^2))/10 + i*sin(sqrt(2)*sqrt(-3 + log(10)^2))/10
Sum and product of roots
[src]
sum
/ _______________\ / _______________\ / _______________\ / _______________\
| ___ / 2 | | ___ / 2 | | ___ / 2 | | ___ / 2 |
cos\\/ 2 *\/ -3 + log (10) / I*sin\\/ 2 *\/ -3 + log (10) / cos\\/ 2 *\/ -3 + log (10) / I*sin\\/ 2 *\/ -3 + log (10) /
----------------------------- - ------------------------------- + ----------------------------- + -------------------------------
10 10 10 10
$$\left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} - \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right) + \left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} + \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right)$$
=
/ _______________\
| ___ / 2 |
cos\\/ 2 *\/ -3 + log (10) /
-----------------------------
5
$$\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{5}$$
product
/ / _______________\ / _______________\\ / / _______________\ / _______________\\ | | ___ / 2 | | ___ / 2 || | | ___ / 2 | | ___ / 2 || |cos\\/ 2 *\/ -3 + log (10) / I*sin\\/ 2 *\/ -3 + log (10) /| |cos\\/ 2 *\/ -3 + log (10) / I*sin\\/ 2 *\/ -3 + log (10) /| |----------------------------- - -------------------------------|*|----------------------------- + -------------------------------| \ 10 10 / \ 10 10 /
$$\left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} - \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right) \left(\frac{\cos{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10} + \frac{i \sin{\left(\sqrt{2} \sqrt{-3 + \log{\left(10 \right)}^{2}} \right)}}{10}\right)$$
=
1/100
$$\frac{1}{100}$$
1/100
Numerical answer
[src]
x1 = -0.0543708526551129 - 0.0839274113836237*i
x2 = -0.0543708526551129 + 0.0839274113836237*i
x2 = -0.0543708526551129 + 0.0839274113836237*i