If-x-2-p-and-y-4-q-then-prove-that-log-2-x-3-y-3p-2q-

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

If x = 2^{p} and y = 4^{q} then prove that

\log_{2} (x^{3} y) = 3 p + 2 q

Answered by AST last updated on 11/Jun/23

{l o g}_{2} (2^{3 p} 2^{2 q}) = {l o g}_{2} (2^{3 p + 2 q}) = 3 p + 2 q

Answered by Frix last updated on 11/Jun/23

{(b^{m})}^{n} = b^{m n}

b^{m} b^{n} = b^{m + n}

\log_{b} b^{a} = a

x^{3} y = 2^{3 p} 4^{q} = 2^{3 p} {(2^{2})}^{q} = 2^{3 p} 2^{2 q} = 2^{3 p + 2 q}

\log_{2} 2^{3 p + 2 q} = 3 p + 2 q

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