2-x-4-y-8-z-and-1-2x-1-1-4y-1-6z-24-7-z-

Question Number 221239 by fantastic last updated on 28/May/25

$$\mathrm{2}^{{x}} =\mathrm{4}^{{y}} =\mathrm{8}^{{z}} \:\:{and}\:\left(\frac{\mathrm{1}}{\mathrm{2}{x}}+\mathrm{1}\frac{\mathrm{1}}{\mathrm{4}{y}}+\frac{\mathrm{1}}{\mathrm{6}{z}}\right)=\frac{\mathrm{24}}{\mathrm{7}}\:\:\: \\ $$$${z}=?? \\ $$

Answered by Rasheed.Sindhi last updated on 28/May/25

$$\mathrm{2}^{{x}} =\mathrm{4}^{{y}} =\mathrm{8}^{{z}} \:\:{and}\:\left(\frac{\mathrm{1}}{\mathrm{2}{x}}+\frac{\mathrm{1}}{\mathrm{4}{y}}+\frac{\mathrm{1}}{\mathrm{6}{z}}\right)=\frac{\mathrm{24}}{\mathrm{7}}\:\:\: \\ $$$${z}=?? \\ $$$$\mathrm{2}^{{x}} =\mathrm{2}^{\mathrm{2}{y}} =\mathrm{2}^{\mathrm{3}{z}} \Rightarrow{x}=\mathrm{2}{y}=\mathrm{3}{z}\Rightarrow\mathrm{2}{x}=\mathrm{4}{y}=\mathrm{6}{z} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{x}}+\frac{\mathrm{1}}{\mathrm{4}{y}}+\frac{\mathrm{1}}{\mathrm{6}{z}}=\frac{\mathrm{24}}{\mathrm{7}} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{6}{z}}+\frac{\mathrm{1}}{\mathrm{6}{z}}+\frac{\mathrm{1}}{\mathrm{6}{z}}=\frac{\mathrm{24}}{\mathrm{7}} \\ $$$$\:\:\:\:\:\mathrm{3}\left(\frac{\mathrm{1}}{\mathrm{6}{z}}\right)=\frac{\mathrm{24}}{\mathrm{7}} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{z}}=\frac{\mathrm{24}}{\mathrm{7}} \\ $$$$\mathrm{2}{z}=\frac{\mathrm{7}}{\mathrm{24}} \\ $$$${z}=\frac{\mathrm{7}}{\mathrm{48}} \\ $$

Commented by fantastic last updated on 28/May/25

$${Right} \\ $$

Commented by fantastic last updated on 28/May/25

$${Thanks}\:{Sir} \\ $$

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