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Question Number 22928 by selestian last updated on 24/Oct/17

Answered by $@ty@m last updated on 24/Oct/17

$$Let{x}^{18}=y^{21}=z^{28}=k$$$$\Rightarrow x=k^{\frac{1}{18}},y=k^{\frac{1}{21}},z=k^{\frac{1}{28}}$$$$\therefore 3\log {}_{y}x=3\frac{\log x}{\log y}=3\frac{\log k^{\frac{1}{18}}}{\log k^{\frac{1}{21}}}$$$$=3\times \frac{\frac{1}{18}}{\frac{1}{21}}=3\times \frac{21}{18}=\frac{7}{2}$$$$Similarly$$$$3\log {}_{z}y=3\times \frac{28}{21}=4$$$$and7\log {}_{x}z=7\times \frac{18}{28}=\frac{9}{2}$$$$3,\frac{7}{2},4,\frac{9}{2}areinAP$$

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