$\frac {n}{θ}+\sum_{i=1}^{n}lnx_i=0$ How to get rid of that summation so I can get my θ estimator?

Question

my question is in the title. Will copy it here as well:

$\ln L(θ) = n \ln θ + (θ − 1)\sum \ln x_i$

$\frac {dlnL}{dθ}=\frac {n}{θ}+\sum_{i=1}^{n}lnx_i$

$\frac {n}{θ}+\sum_{i=1}^{n}lnx_i=0$

How to get rid of that summation so I can get my $\hat θ$ estimator?

Thanks!

Answer 1

$$\frac{n}{\hat{\theta}}+\sum_{i=1} \ln x_i = 0$$

$$\frac{n}{\hat{\theta}}=-\sum_{i=1} \ln x_i $$

$$\frac{n}{-\sum_{i=1} \ln x_i }=\hat{\theta}$$