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dedylja [7]
3 years ago
7

Expand the log as a sun or difference

Mathematics
2 answers:
Hitman42 [59]3 years ago
5 0
27. (1/2*log(9) -(4*log(x) +1/3*log(3))/log(a)
  = ((1/2)*2*log(3) -4*log(x) -1/3*log(3))/log(a)
  = ((2/3)*log(3) -4*log(x))/log(a)
  = \frac{2}{3}\log_a{(3)}-4\log_a{(x)}
snow_lady [41]3 years ago
4 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 log_a\left( \cfrac{9^{\frac{1}{2}}}{x^43^{\frac{1}{3}}} \right)\implies log_a\left( 9^{\frac{1}{2}} \right)-log_a\left( x^43^{\frac{1}{3}} \right)
\\\\\\
log_a\left( 9^{\frac{1}{2}} \right)-\left[ log_a\left( x^4 \right)+log_a\left( 3^{\frac{1}{3}} \right) \right] 
\\\\\\
log_a\left( 9^{\frac{1}{2}} \right)-log_a\left( x^4 \right)-log_a\left( 3^{\frac{1}{3}} \right)\\\\\\ \cfrac{1}{2}log_a(9)-4log_a(x)-\cfrac{1}{3}log_a(3)

or more expanded so as 

\bf \cfrac{1}{2}log_a(3^2)-4log_a(x)-\cfrac{1}{3}log_a(3)
\\\\\\
\cfrac{1}{2}\cdot  2log_a(3)-4log_a(x)-\cfrac{1}{3}log_a(3)
\\\\\\ log_a(3)-4log_a(x)-\cfrac{1}{3}log_a(3)
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Step-by-step explanation:

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_____

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Since this answer does not correspond to any of the offered choices, we suggest you ask your teacher to work this out for you. We suspect they will have difficulty justifying any of the answer choices shown here. (0.11 lb corresponds to 4 washers, not 5.)

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