Mister Exam
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How to use it?
- Equation:
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Equation -x=4-3(3x-8)
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Equation x/9+x=-10/3
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Equation √(x^2-1)=2*x
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Equation 4(x-3)=x+6
- Express {x} in terms of y where:
- -6*x-20*y=8
- -9*x-15*y=-4
- 1*x+5*y=-11
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Identical expressions
- three + two *log(x+ one)* three = two *log3*(x+ one)
- 3 plus 2 multiply by logarithm of (x plus 1) multiply by 3 equally 2 multiply by logarithm of 3 multiply by (x plus 1)
- three plus two multiply by logarithm of (x plus one) multiply by three equally two multiply by logarithm of 3 multiply by (x plus one)
- 3+2log(x+1)3=2log3(x+1)
- 3+2logx+13=2log3x+1
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Similar expressions
- 3+2*log(x-1)*3=2*log3*(x+1)
- 3+2*log(x+1)*3=2*log3*(x-1)
- 3-2*log(x+1)*3=2*log3*(x+1)
3+2*log(x+1)*3=2*log3*(x+1) equation
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The solution
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[src]
3 + 2*log(x + 1)*3 = 2*log(3)*(x + 1)
$$3 \cdot 2 \log{\left(x + 1 \right)} + 3 = \left(x + 1\right) 2 \log{\left(3 \right)}$$
Rapid solution
[src]
/ -1/2 \
|-e *log(3) |
3*W|--------------|
\ 3 /
x1 = -1 - -------------------
log(3)
$$x_{1} = -1 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}$$
/ -1/2 \
|-e *log(3) |
3*W|--------------, -1|
\ 3 /
x2 = -1 - -----------------------
log(3)
$$x_{2} = -1 - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}$$
x2 = -1 - 3*LambertW(-exp(-1/2)*log(3/3, -1)/log(3))
Sum and product of roots
[src]
sum
/ -1/2 \ / -1/2 \
|-e *log(3) | |-e *log(3) |
3*W|--------------| 3*W|--------------, -1|
\ 3 / \ 3 /
-1 - ------------------- + -1 - -----------------------
log(3) log(3)
$$\left(-1 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right) + \left(-1 - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right)$$
=
/ -1/2 \ / -1/2 \
|-e *log(3) | |-e *log(3) |
3*W|--------------| 3*W|--------------, -1|
\ 3 / \ 3 /
-2 - ------------------- - -----------------------
log(3) log(3)
$$-2 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}} - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}$$
product
/ / -1/2 \\ / / -1/2 \\ | |-e *log(3) || | |-e *log(3) || | 3*W|--------------|| | 3*W|--------------, -1|| | \ 3 /| | \ 3 /| |-1 - -------------------|*|-1 - -----------------------| \ log(3) / \ log(3) /
$$\left(-1 - \frac{3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right) \left(-1 - \frac{3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right)}{\log{\left(3 \right)}}\right)$$
=
/ / -1/2 \ \ / / -1/2 \ \
| |-e *log(3) | | | |-e *log(3) | |
|3*W|--------------| + log(3)|*|3*W|--------------, -1| + log(3)|
\ \ 3 / / \ \ 3 / /
-----------------------------------------------------------------
2
log (3)
$$\frac{\left(3 W\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right) + \log{\left(3 \right)}\right) \left(3 W_{-1}\left(- \frac{\log{\left(3 \right)}}{3 e^{\frac{1}{2}}}\right) + \log{\left(3 \right)}\right)}{\log{\left(3 \right)}^{2}}$$
(3*LambertW(-exp(-1/2)*log(3)/3) + log(3))*(3*LambertW(-exp(-1/2)*log(3)/3, -1) + log(3))/log(3)^2