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mixer [17]
3 years ago
8

Question #12 Please help

Mathematics
1 answer:
julia-pushkina [17]3 years ago
7 0
\bf \textit{logarithm of factors}\\\\
log_a(xy)\implies log_a(x)+log_a(y)
\\\\\\
\textit{Logarithm of rationals}\\\\
log_a\left(  \frac{x}{y}\right)\implies log_a(x)-log_a(y)
\\\\\\
\textit{Logarithm of exponentials}\\\\
log_a\left( x^  b \right)\implies   b\cdot  log_a(x)\\\\
-------------------------------\\\\


\bf a)\\\\
log_9\left( \sqrt[3]{y^2+y} \right)\implies log_9\left[ (y^2+y)^{\frac{1}{3}} \right]\implies \cfrac{1}{3}log_9(y^2+y)
\\\\\\
\cfrac{1}{3}log_9[y(y+1)]\implies \cfrac{1}{3}\left[~log_9(y)~+~log_9(y+1) ~ \right]
\\\\\\
\cfrac{1}{3}log_9(y)~~+~~\cfrac{1}{3}log_9(y+1)


\bf b)\\\\
log_4\left( \frac{a^2b}{\sqrt{c}} \right)\implies log_4(a^2b)~-~log_4(\sqrt{c})\implies log_4(a^2b)~-~log_4(c^{\frac{1}{2}})
\\\\\\\
[~log_4(a^2)~+log_4(b)~]~~-~~\cfrac{1}{2}log_4(c)\\\\\\ log_4(a^2)+log_4(b)-\cfrac{1}{2}log_4(c)
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