# Suppose that x = log A and y = log B. i need to write these expressions in terms of x and y log(AB) log(A^3 times sqrt(B)) log(A-B)

chivistaelmore 2022-07-28 Answered
Suppose that $x=\mathrm{log}A$ and $y=\mathrm{log}B$. i need to write these expressions in terms of x and y
$\mathrm{log}\left(AB\right)$
$\mathrm{log}\left({A}^{3}×\sqrt{B}\right)$
$\mathrm{log}\left(A-B\right)$
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## Answers (1)

Minbutastc
Answered 2022-07-29 Author has 14 answers
$\mathrm{log}\left(AB\right)=\mathrm{log}A+\mathrm{log}B=x+y$
$\mathrm{log}\left({A}^{3}\sqrt{B}\right)=\mathrm{log}{A}^{3}+\mathrm{log}\sqrt{B}=3\mathrm{log}A+\frac{1}{2}\mathrm{log}B=3x+\frac{1}{2}y$
$\mathrm{log}\left(A-B\right)$ cant break it out
only work if it's $\mathrm{log}\left(A\right)-\mathrm{log}B=\mathrm{log}\frac{A}{B}$

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