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Question Number 212976 by hardmath last updated on 27/Oct/24

$$4^{\mathbf{x}}=125\mathrm{and}{8}^{\mathbf{y}}=5$$$$\mathrm{find}:\frac{2\mathrm{x}-\mathrm{y}}{\mathrm{y}}=?$$

Answered by Amiltonsad last updated on 27/Oct/24

$$$$$$how{4}^x=125\Rightarrow 2^{2x}=5^{3}and{\left(2\right)}^{\frac{2x}{3}}=5$$$$andhow...8^y=52^{3y}=5$$$$$$$$finallywecansay\frac{2x-y}{y}=\frac{9y-y}{y}=\frac{8y}{y}=8$$$$answeredbyAlfadosALFAS$$

Answered by A5T last updated on 27/Oct/24

$$x={log}_{4}125=\frac{3}{2}{log}_{2}5;y={log}_{8}5=\frac{{log}_{2}5}{3}$$$$\Rightarrow \frac{2x-y}{y}=\frac{2x}{y}-1=\frac{3{log}_{2}5}{\frac{{log}_{2}5}{3}}-1=8$$

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