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AleksandrR [38]
3 years ago
7

Write the expression as a single logarithm PLEASE (log3-log4)-log2

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
4 0

\bf \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\[1em] [\log(3)-\log(4)]-\log(2)\implies \log\left( \cfrac{3}{4} \right)-\log(2)\implies \log\left( \cfrac{\frac{3}{4}}{~~2~~} \right) \\\\\\ \log\left( \cfrac{\frac{3}{4}}{~~\frac{2}{1}~~} \right)\implies \log\left( \cfrac{3}{4}\cdot \cfrac{1}{2} \right)\implies \log\left( \cfrac{3}{8} \right)

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If a copier contains 60% letter-size paper and 40% legal-size paper, what is the ratio of letter-size paper to legal-size paper?
Vladimir79 [104]

Answer:

The ratio is 3/2 or 3:2

Step-by-step explanation:

we know that

To find out the ratio of letter-size paper to legal-size paper, divide the percentage of letter-size paper by the percentage of legal-size paper

so

\frac{60}{40}

Simplify

\frac{60}{40}=\frac{6}{4}=\frac{3}{2}

therefore

The ratio is 3/2 or 3:2

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Which expression is the product of (x + 4i)(x − 4i)(x + 4)?
Sophie [7]
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Expand the following:(x + 4 i) (x - 4 i) (x + 4)
(x - 4 i) (x + 4) = (x) (x) + (x) (4) + (-4 i) (x) + (-4 i) (4) = x^2 + 4 x - 4 i x - 16 i = -16 i + (4 - 4 i) x + x^2:
-16 i + (-4 i + 4) x + x^2 (4 i + x)
 | | | | x | + | 4 i
 | | x^2 | + | (4 - 4 i) x | - | 16 i
 | | | | (-16 i) x | + | 64
 | | (4 - 4 i) x^2 | + | (16 + 16 i) x | + | 0
x^3 | + | (4 i) x^2 | + | 0 | + | 0
x^3 | + | 4 x^2 | + | 16 x | + | 64:
Answer: x^3 + 4 x^2 + 16 x + 64
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Y=x+1

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