Question Number 205496 by cortano12 last updated on 22/Mar/24
Answered by Frix last updated on 22/Mar/24
$${x}>\mathrm{0} \\ $$$${t}=\sqrt[{\mathrm{3}}]{{x}} \\ $$$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{1}+{t}\right)\:=\mathrm{3log}_{\mathrm{7}} \:{x} \\ $$$$\mathrm{Obviously}\:{t}=\mathrm{7} \\ $$$${x}=\mathrm{7}^{\mathrm{3}} =\mathrm{343} \\ $$$$\mathrm{If}\:\mathrm{there}\:\mathrm{was}\:\mathrm{no}\:\mathrm{obvious}\:\mathrm{solution}\:\mathrm{we}\:\mathrm{could} \\ $$$$\mathrm{only}\:\mathrm{approximate}. \\ $$