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Question Number 132368 by otchereabdullai@gmail.com last updated on 13/Feb/21

$$\mathrm{Show}\mathrm{that}{\log }_{2}5.{\log }_{4}3.{\log }_{25}16={\log }_{2}3$$

Answered by mr W last updated on 13/Feb/21

$$generally{\log }_{a}b=\frac{{\log }_{c}b}{{\log }_{c}a}$$$${\log }_{2}5.{\log }_{4}3.{\log }_{25}16$$$$=\frac{{\log }_{2}5}{{\log }_{2}2}\times \frac{{\log }_{2}3}{{\log }_{2}4}\times \frac{{\log }_{2}16}{{\log }_{2}25}$$$$=\frac{\cancel{{\log }_{2}5}}{{\log }_{2}2}\times \frac{{\log }_{2}3}{{2\log }_{2}2}\times \frac{{4\log }_{2}2}{2\cancel{{\log }_{2}5}}$$$$=\frac{1}{1}\times \frac{{\log }_{2}3}{2}\times \frac{4}{2}$$$$={\log }_{2}3$$

Commented by otchereabdullai@gmail.com last updated on 13/Feb/21

$$\mathrm{you}\mathrm{are}\mathrm{always}\mathrm{my}\mathrm{prof}!\mathrm{If}\mathrm{something}$$$$\mathrm{is}\mathrm{more}\mathrm{than}\mathrm{blessing}\mathrm{God}\mathrm{should}\mathrm{give}$$$$\mathrm{it}\mathrm{to}\mathrm{you}$$

Commented by mr W last updated on 14/Feb/21

$$Godblessyoutoo!$$

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