How do you expand $ln (\frac{x}{y}) - 2 ln (x^{3}) - 4 ln y$ $ln(x/y) - 2ln(x^3) -4lny$ ?

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How do you expand $ln (\frac{x}{y}) - 2 ln (x^{3}) - 4 ln y$ $ln(x/y) - 2ln(x^3) -4lny$ ?

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Answer 1 · 2016-05-19T17:23:47

Answer:
after expanding $- 5 ln x - 5 ln y$ $-5lnx-5lny$
after simplication $- {ln (x y)}^{5}$ $-ln(xy)^5$

Explanation:

$ln (\frac{A}{B}) = ln A - ln B$ $ln(A/B) = ln A - ln B$
$ln (A B) = ln A + ln B$ $ln(AB) = lnA+lnB$
$ln (A^{B}) = B \cdot ln A$ $ln(A^B) = B*lnA$

Using the above two rules we can expand the given expression into:

$ln x - ln y - 2 \cdot 3 \cdot ln x - 4 ln y$ $lnx - lny -2*3*lnx-4lny$
$\Rightarrow ln x - ln y - 6 ln x - 4 ln y$ $rArrlnx-lny-6lnx-4lny$
$or, - 5 ln x - 5 ln y$ $or, -5lnx-5lny$

On further simplification we get

$- 5 (ln x + ln y)$ $-5(lnx +lny)$
$or - 5 \cdot ln x y$ $or-5*lnxy$
$or - {ln (x y)}^{5}$ $or-ln(xy)^5$

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How do you expand $ln (\frac{x}{y}) - 2 ln (x^{3}) - 4 ln y$ $ln(x/y) - 2ln(x^3) -4lny$ ?

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Explanation:

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How do you expand ln(xy)−2ln(x3)−4lny ln(x/y) - 2ln(x^3) -4lny ?

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Explanation:

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How do you expand $ln (\frac{x}{y}) - 2 ln (x^{3}) - 4 ln y$ $ln(x/y) - 2ln(x^3) -4lny$ ?