ln(x)=0.5x equation

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

You have entered [src]

         x
log(x) = -
         2

$$\log{\left(x \right)} = \frac{x}{2}$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

x1 = -2*re(W(-1/2)) - 2*I*im(W(-1/2))

$$x_{1} = - 2 \operatorname{re}{\left(W\left(- \frac{1}{2}\right)\right)} - 2 i \operatorname{im}{\left(W\left(- \frac{1}{2}\right)\right)}$$

x1 = -2*re(LambertW(-1/2)) - 2*i*im(LambertW(-1/2))

Sum and product of roots [src]

sum

-2*re(W(-1/2)) - 2*I*im(W(-1/2))

$$- 2 \operatorname{re}{\left(W\left(- \frac{1}{2}\right)\right)} - 2 i \operatorname{im}{\left(W\left(- \frac{1}{2}\right)\right)}$$

-2*re(W(-1/2)) - 2*I*im(W(-1/2))

$$- 2 \operatorname{re}{\left(W\left(- \frac{1}{2}\right)\right)} - 2 i \operatorname{im}{\left(W\left(- \frac{1}{2}\right)\right)}$$

product

-2*re(W(-1/2)) - 2*I*im(W(-1/2))

$$- 2 \operatorname{re}{\left(W\left(- \frac{1}{2}\right)\right)} - 2 i \operatorname{im}{\left(W\left(- \frac{1}{2}\right)\right)}$$

-2*re(W(-1/2)) - 2*I*im(W(-1/2))

$$- 2 \operatorname{re}{\left(W\left(- \frac{1}{2}\right)\right)} - 2 i \operatorname{im}{\left(W\left(- \frac{1}{2}\right)\right)}$$

-2*re(LambertW(-1/2)) - 2*i*im(LambertW(-1/2))

Numerical answer [src]

x1 = 1.58804726468938 + 1.54022350102076*i

x1 = 1.58804726468938 + 1.54022350102076*i