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Question Number 199230 by hardmath last updated on 29/Oct/23

$$\mathrm{x},\mathrm{y}:\mathrm{positive}\mathrm{real}\mathrm{numbers}$$$$\mathrm{If}:{15}^{\mathbf{x}}=9^{\mathbf{y}}$$$$\mathrm{Find}:5^{\frac{3\mathbf{x}}{2\mathbf{y}-\mathbf{x}}}=?$$

Answered by deleteduser1 last updated on 29/Oct/23

$$3^x{5}^x=3^{2y}\Rightarrow 5^x=3^{2y-x}\Rightarrow 5^{\frac{3x}{2y-x}}=3^3=27$$

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