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Question Number 193360 by MATHEMATICSAM last updated on 11/Jun/23

$$\mathrm{If}x=2^p\mathrm{and}y=4^q\mathrm{then}\mathrm{prove}\mathrm{that}$$$${\log }_2\left(x^{3}y\right)=3p+2q$$

Answered by deleteduser1 last updated on 11/Jun/23

$${log}_2\left(2^{3p}{2}^{2q}\right)={log}_2\left(2^{3p+2q}\right)=3p+2q$$

Answered by Frix last updated on 11/Jun/23

$${\left(b^m\right)}^n=b^{mn}$$$$b^m{b}^n=b^{m+n}$$$${\log }_b{b}^a=a$$$$$$$$x^{3}y=2^{3p}{4}^q=2^{3p}{\left(2^2\right)}^q=2^{3p}{2}^{2q}=2^{3p+2q}$$$${\log }_2{2}^{3p+2q}=3p+2q$$

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