Question Number 54013 by zambolly19 last updated on 27/Jan/19
$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} =−\mathrm{4}.\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}} \\ $$
Answered by Smail last updated on 27/Jan/19
$${xln}\mathrm{2}={ln}\left(−\mathrm{4}\right) \\ $$$${x}=\frac{{ln}\left(\mathrm{4}{e}^{{i}\pi} \right)}{{ln}\mathrm{2}}=\frac{\mathrm{2}{ln}\mathrm{2}+{i}\pi}{{ln}\mathrm{2}}=\mathrm{2}+{i}\frac{\pi}{{ln}\mathrm{2}} \\ $$$${x}=\mathrm{2}+\frac{{i}\pi}{{ln}\mathrm{2}} \\ $$