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Gemiola [76]
4 years ago
15

Can someone help me in #66

Mathematics
1 answer:
VladimirAG [237]4 years ago
6 0
\bf log_{{  a}}(xy)\implies log_{{  a}}(x)+log_{{  a}}(y)
\\ \quad \\
% Logarithm of rationals
log_{{  a}}\left(  \frac{x}{y}\right)\implies log_{{  a}}(x)-log_{{  a}}(y)
\\ \quad \\
% Logarithm of exponentials
log_{{  a}}\left( x^{{  b}} \right)\implies {{  b}}\cdot  log_{{  a}}(x)\\\\
-------------------------------\\\\


\bf log_4\left( \cfrac{\sqrt{x^5y^7}}{zw^4} \right)\implies log_4(\sqrt{x^5y^7})-log_4(zw^4)
\\\\\\
log_4\left[(x^5y^7)^{^\frac{1}{2}}\right]-log_4(zw^4)\implies 
\cfrac{1}{2}log_4\left[(x^5y^7)\right]-log_4(zw^4)
\\\\\\
\cfrac{1}{2}\left[ log_4(x^5)+log_4(y^7) \right] -[log_4(z)+log_4(w^4)]
\\\\\\
\cfrac{1}{2}log_4(x^5)+\cfrac{1}{2}log_4(y^7)-[log_4(z)+log_4(w^4)]

\bf \cfrac{1}{2}\cdot 5log_4(x)+\cfrac{1}{2}\cdot 7log_4(y)-log_4(z)-4log_4(w)
\\\\\\
\cfrac{5}{2}log_4(x)+\cfrac{7}{2}log_4(y)-log_4(z)-4log_4(w)
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