What is simplify-ln|0-3|+2ln|0-2| ?

The solution to simplify-ln|0-3|+2ln|0-2| is ln(4/3)

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simplify-ln|0-3|+2ln|0-2|

simplify

- ln ∣ 0 - 3 ∣ + 2 ln ∣ 0 - 2 ∣

ln (\frac{4}{3})

Decimal Notation

0.28768 \dots

Solution steps

- ln ∣ 0 - 3 ∣ + 2 ln ∣ 0 - 2 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln ∣ 0 - 2 ∣ = ln (∣ 0 - 2 ∣^{2})

= - ln ∣ 0 - 3 ∣ + ln (∣ 0 - 2 ∣^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (∣ 0 - 2 ∣^{2}) - ln ∣ 0 - 3 ∣ = ln (\frac{∣ 0 - 2 ∣ ^{2}}{∣ 0 - 3 ∣})

= ln (\frac{∣ 0 - 2 ∣ ^{2}}{∣ 0 - 3 ∣})

\frac{∣ 0 - 2 ∣ ^{2}}{∣ 0 - 3 ∣} = \frac{4}{3}

= ln (\frac{4}{3})

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What is simplify-ln|0-3|+2ln|0-2| ?
The solution to simplify-ln|0-3|+2ln|0-2| is ln(4/3)