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Write as a single logarithm

Write as a single logarithm-example-1
User Leypascua
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ANSWER


c. \ln( \frac{2 {x}^(3) }{3y})

Step-by-step explanation

We want to write


ln(2x) + 2 ln(x) - ln(3y)

as a single logarithm.

Use the power rule to rewrite the middle term:


n \: ln(a) = ln( {a}^(n) )


ln(2x) + ln( {x}^(2) ) - ln(3y)

Use the product rule to obtain:


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


ln(2x * {x}^(2) )- ln(3y)


ln(2{x}^(3) )- ln(3y)

Apply the quotient rule:


ln(a) - ln(b) = ln( (a)/(b))


ln(2{x}^(3) )- ln(3y) =\ln(\frac{2 {x}^(3) }{3y})

User JivanAmara
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