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Popular >

simplify ln|5|-2ln|2|

Solution

simplify

ln ∣ 5 ∣ - 2 ln ∣ 2 ∣

Solution

ln (\frac{5}{4})

+1

Decimal

0.22314 \dots

Solution steps

ln ∣ 5 ∣ - 2 ln ∣ 2 ∣

Apply log rule:

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

2 ln ∣ 2 ∣ = ln (∣ 2 ∣^{2})

= ln ∣ 5 ∣ - ln (∣ 2 ∣^{2})

Apply log rule:

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

ln ∣ 5 ∣ - ln (∣ 2 ∣^{2}) = ln (\frac{∣ 5 ∣}{∣ 2 ∣ ^{2}})

= ln (\frac{∣ 5 ∣}{∣ 2 ∣ ^{2}})

\frac{∣ 5 ∣}{∣ 2 ∣ ^{2}} = \frac{5}{4}

= ln (\frac{5}{4})

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Frequently Asked Questions (FAQ)

What is ln|5|-2ln|2| ?
The solution to ln|5|-2ln|2| is ln(5/4)