Question Number 70252 by Shamim last updated on 02/Oct/19
$$\mathrm{If},\:\mathrm{log}\:\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{6}\:\mathrm{and}\:\mathrm{log}\:\mathrm{14x}^{\mathrm{8y}} \:=\:\mathrm{3}\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x},\:\mathrm{y}. \\ $$
Answered by MJS last updated on 02/Oct/19
$$\mathrm{log}\:{x}^{{y}} =\mathrm{6}\:\Rightarrow\:{y}\mathrm{log}\:{x}\:=\mathrm{6} \\ $$$$\mathrm{log}\:\mathrm{14}{x}^{\mathrm{8}{y}} \:=\mathrm{3}\:\Rightarrow\:\mathrm{log}\:\mathrm{14}\:+\mathrm{8}{y}\mathrm{log}\:{x}\:=\mathrm{3} \\ $$$$\mathrm{let}\:{y}\mathrm{log}\:{x}\:={z} \\ $$$${z}=\mathrm{6} \\ $$$${z}=\frac{\mathrm{3}−\mathrm{log}\:\mathrm{14}}{\mathrm{8}} \\ $$$$\Rightarrow\:\mathrm{no}\:\mathrm{solution} \\ $$
Commented by Shamim last updated on 02/Oct/19
$$\mathrm{yes}.\:\mathrm{i}\:\mathrm{get}\:\mathrm{this}\:\mathrm{same}\:\mathrm{result}.\:\mathrm{so}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{is}\:\mathrm{wrong}???? \\ $$
Commented by mind is power last updated on 02/Oct/19
$${i}\:{thonk}\:{is}\:{log}\left(\mathrm{14}{x}\right)^{\mathrm{8}{y}} \\ $$
Commented by Shamim last updated on 03/Oct/19
$$\mathrm{plz}\:\mathrm{solve} \\ $$