Question Number 152349 by otchereabdullai@gmail.com last updated on 27/Aug/21
$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}_{\mathrm{8x}\:} \:,\:\mathrm{find}\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{2}\right) \\ $$
Commented by otchereabdullai@gmail.com last updated on 27/Aug/21
$$\mathrm{Exactly}\:\mathrm{prof}\:\mathrm{W}\:\mathrm{typo}\:\mathrm{error}\:.\:\mathrm{Am}\:\mathrm{much} \\ $$$$\mathrm{grateful}\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}!\: \\ $$
Commented by mr W last updated on 27/Aug/21
$${i}\:{think}\:{you}\:{meant}\:{f}\left({x}\right)=\mathrm{log}_{\mathrm{8}} \:{x}. \\ $$$${y}=\mathrm{log}_{\mathrm{8}} \:{x} \\ $$$$\Rightarrow{x}=\mathrm{8}^{{y}} \\ $$$$\Rightarrow{f}^{−\mathrm{1}} \left({x}\right)=\mathrm{8}^{{x}} \\ $$$$\Rightarrow{f}^{−\mathrm{1}} \left(\mathrm{2}\right)=\mathrm{8}^{\mathrm{2}} =\mathrm{64} \\ $$