Express in terms of sums and differences of logarithms

Ответ:

jahzz

04.01.2022

ANSWER

$ln( \frac{9}{8 {x}^{8}y } ) =2ln( {3}) -( 3 ln( {2}) +8 ln( {x}) + ln( y ) )$

EXPLANATION

The given logarithmic expression is:

$ln( \frac{9}{8 {x}^{8}y } )$

Recall and apply the quotient rule:

$ln( \frac{a}{b} ) = ln(a) - ln(b)$

This gives;

$ln( \frac{9}{8 {x}^{8}y } ) = ln( 9 ) - ln( 8 {x}^{8}y )$

Use the product rule:

ln(ab) = ln(a) + ln(b)

$ln( \frac{9}{8 {x}^{8}y } ) = ln( 9 ) -( ln( 8 ) + ln( {x}^{8}) + ln( y ) )$

$ln( \frac{9}{8 {x}^{8}y } ) = ln( {3}^{2} ) -( ln( {2}^{3} ) + ln( {x}^{8}) + ln( y ) )$

Apply the power rule:

$ln( {a}^{k} ) = k \: ln(a)$

$ln( \frac{9}{8 {x}^{8}y } ) =2ln( {3}) -( 3 ln( {2}) +8 ln( {x}) + ln( y ) )$

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Ответ:

nathansnyder200

24.01.2021

Mathematics

rawr xd xd npoo b

Step-by-step explanation:

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Express in terms of sums and differences of logarithms ln 9/8x^8 y

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