Mister Exam

Lang:

x*ln(6)-ln(x/pi)=0 equation

The teacher will be very surprised to see your correct solution 😉

You have entered [src]

              /x \    
x*log(6) - log|--| = 0
              \pi/

x \log{\left(6 \right)} - \log{\left(\frac{x}{\pi} \right)} = 0

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

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