Question Number 199230 by hardmath last updated on 29/Oct/23
$$\mathrm{x}\:,\:\mathrm{y}\::\:\:\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{If}\::\:\:\:\mathrm{15}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{9}^{\boldsymbol{\mathrm{y}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{5}^{\frac{\mathrm{3}\boldsymbol{\mathrm{x}}}{\mathrm{2}\boldsymbol{\mathrm{y}}\:−\:\boldsymbol{\mathrm{x}}}} \:\:=\:\:? \\ $$
Answered by AST last updated on 29/Oct/23
$$\mathrm{3}^{{x}} \mathrm{5}^{{x}} =\mathrm{3}^{\mathrm{2}{y}} \Rightarrow\mathrm{5}^{{x}} =\mathrm{3}^{\mathrm{2}{y}−{x}} \Rightarrow\mathrm{5}^{\frac{\mathrm{3}{x}}{\mathrm{2}{y}−{x}}} =\mathrm{3}^{\mathrm{3}} =\mathrm{27} \\ $$