Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5*sin(x)+cos(x)=5
-
Equation 4*x^2+7=7+24*x
-
Equation 2x^2-3x-2=0
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Equation x^2-7*x+10=0
- Express {x} in terms of y where:
- 17*x-19*y=-12
- 3*x+19*y=4
- 13*x-1*y=-20
- -16*x-9*y=-1
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Identical expressions
- zero , eight ^x= five ^ one -2x
- 0,008 to the power of x equally 5 to the power of 1 minus 2x
- zero , eight to the power of x equally five to the power of one minus 2x
- 0,008x=51-2x
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Similar expressions
- 0,008^x=5^1+2x
0,008^x=5^1-2x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
/ / ___\\
| | 3*\/ 5 ||
| | -------||
| | 781250||
2*W\-log\5 // + log(30517578125)
x1 = --------------------------------------
6*log(5)
$$x_{1} = \frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}$$
/ / ___\ \
| | 3*\/ 5 | |
| | -------| |
| | 781250| |
2*W\-log\5 /, -1/ + log(30517578125)
x2 = ------------------------------------------
6*log(5)
$$x_{2} = \frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}$$
x2 = (2*LambertW(-log(5^(3*sqrt(5)/781250), -1) + log(30517578125))/(6*log(5)))
Sum and product of roots
[src]
sum
/ / ___\\ / / ___\ \
| | 3*\/ 5 || | | 3*\/ 5 | |
| | -------|| | | -------| |
| | 781250|| | | 781250| |
2*W\-log\5 // + log(30517578125) 2*W\-log\5 /, -1/ + log(30517578125)
-------------------------------------- + ------------------------------------------
6*log(5) 6*log(5)
$$\frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}} + \frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}$$
=
/ / ___\\ / / ___\ \
| | 3*\/ 5 || | | 3*\/ 5 | |
| | -------|| | | -------| |
| | 781250|| | | 781250| |
2*W\-log\5 // + log(30517578125) 2*W\-log\5 /, -1/ + log(30517578125)
-------------------------------------- + ------------------------------------------
6*log(5) 6*log(5)
$$\frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}} + \frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}$$
product
/ / ___\\ / / ___\ \
| | 3*\/ 5 || | | 3*\/ 5 | |
| | -------|| | | -------| |
| | 781250|| | | 781250| |
2*W\-log\5 // + log(30517578125) 2*W\-log\5 /, -1/ + log(30517578125)
--------------------------------------*------------------------------------------
6*log(5) 6*log(5)
$$\frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}} \frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}$$
=
/ / / ___\\ \ / / / ___\ \ \
| | | 3*\/ 5 || | | | | 3*\/ 5 | | |
| | | -------|| | | | | -------| | |
| | | 781250|| | | | | 781250| | |
\2*W\-log\5 // + log(30517578125)/*\2*W\-log\5 /, -1/ + log(30517578125)/
-------------------------------------------------------------------------------------
2
36*log (5)
$$\frac{\left(2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}\right) \left(2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}\right)}{36 \log{\left(5 \right)}^{2}}$$
(2*LambertW(-log(5^(3*sqrt(5)/781250))) + log(30517578125))*(2*LambertW(-log(5^(3*sqrt(5)/781250)), -1) + log(30517578125))/(36*log(5)^2)