Mister Exam
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How to use it?
- Equation:
-
Equation 6*x^2+x-7=0
-
Equation (x^2-9)^2+(x^2+x-6)^2=0
-
Equation sin(2*x-pi/3)=0
-
Equation x/(75/5)=60
- Express {x} in terms of y where:
- 16*x+12*y=-13
- -1*x+5*y=15
- -8*x+8*y=-6
- -19*x-18*y=-6
-
Identical expressions
- x*ln(six)-ln(x/pi)= zero
- x multiply by ln(6) minus ln(x divide by Pi ) equally 0
- x multiply by ln(six) minus ln(x divide by Pi ) equally zero
- xln(6)-ln(x/pi)=0
- xln6-lnx/pi=0
- x*ln(6)-ln(x/pi)=O
- x*ln(6)-ln(x divide by pi)=0
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Similar expressions
- x*ln(6)+ln(x/pi)=0
x*ln(6)-ln(x/pi)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x \
x*log(6) - log|--| = 0
\pi/
$$x \log{\left(6 \right)} - \log{\left(\frac{x}{\pi} \right)} = 0$$
Rapid solution
[src]
re(W(-pi*log(6))) I*im(W(-pi*log(6)))
x1 = - ----------------- - -------------------
log(6) log(6)
$$x_{1} = - \frac{\operatorname{re}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}}$$
x1 = -re(LambertW(-pi*log(6)))/log(6) - i*im(LambertW(-pi*log(6)))/log(6)
Sum and product of roots
[src]
sum
re(W(-pi*log(6))) I*im(W(-pi*log(6)))
- ----------------- - -------------------
log(6) log(6)
$$- \frac{\operatorname{re}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}}$$
=
re(W(-pi*log(6))) I*im(W(-pi*log(6)))
- ----------------- - -------------------
log(6) log(6)
$$- \frac{\operatorname{re}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}}$$
product
re(W(-pi*log(6))) I*im(W(-pi*log(6)))
- ----------------- - -------------------
log(6) log(6)
$$- \frac{\operatorname{re}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}} - \frac{i \operatorname{im}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}}$$
=
-(I*im(W(-pi*log(6))) + re(W(-pi*log(6))))
-------------------------------------------
log(6)
$$- \frac{\operatorname{re}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)} + i \operatorname{im}{\left(W\left(- \pi \log{\left(6 \right)}\right)\right)}}{\log{\left(6 \right)}}$$
-(i*im(LambertW(-pi*log(6))) + re(LambertW(-pi*log(6))))/log(6)
Numerical answer
[src]
x1 = -0.521061360978882 + 1.1197540183224*i
x1 = -0.521061360978882 + 1.1197540183224*i