Question Number 19134 by chernoaguero@gmail.com last updated on 05/Aug/17
$$\mathrm{If}\:\frac{\mathrm{1}}{\left(\mathrm{243}\right)^{{x}} }\:=\:\left(\mathrm{729}\right)^{{y}} =\:\mathrm{3}^{\mathrm{3}} ,\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{5}{x}\:+\:\mathrm{6}{y}. \\ $$
Answered by Tinkutara last updated on 05/Aug/17
$$\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{5}{x}} }\:=\:\mathrm{3}^{\mathrm{3}} \:\Rightarrow\:\mathrm{5}{x}\:=\:−\mathrm{3} \\ $$$$\mathrm{3}^{\mathrm{6}{y}} \:=\:\mathrm{3}^{\mathrm{3}} \:\Rightarrow\:\mathrm{6}{y}\:=\:\mathrm{3} \\ $$$$\mathrm{5}{x}\:+\:\mathrm{6}{y}\:=\:\mathrm{3}\:−\:\mathrm{3}\:=\:\mathrm{0} \\ $$
Commented by chernoaguero@gmail.com last updated on 05/Aug/17
$${thankx}\:{sir} \\ $$