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Popular >

simplify 3ln|5|-3ln|2|

Solution

simplify

3 ln ∣ 5 ∣ - 3 ln ∣ 2 ∣

Solution

ln (\frac{125}{8})

+1

Decimal Notation

2.74887 \dots

Solution steps

3 ln ∣ 5 ∣ - 3 ln ∣ 2 ∣

Apply log rule:

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

3 ln ∣ 5 ∣ = ln (∣ 5 ∣^{3})

= ln (∣ 5 ∣^{3}) - 3 ln ∣ 2 ∣

Apply log rule:

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

3 ln ∣ 2 ∣ = ln (∣ 2 ∣^{3})

= ln (∣ 5 ∣^{3}) - ln (∣ 2 ∣^{3})

Apply log rule:

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

ln (∣ 5 ∣^{3}) - ln (∣ 2 ∣^{3}) = ln (\frac{∣ 5 ∣ ^{3}}{∣ 2 ∣ ^{3}})

= ln (\frac{∣ 5 ∣ ^{3}}{∣ 2 ∣ ^{3}})

\frac{∣ 5 ∣ ^{3}}{∣ 2 ∣ ^{3}} = \frac{125}{8}

= ln (\frac{125}{8})

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Frequently Asked Questions (FAQ)

What is 3ln|5|-3ln|2| ?
The solution to 3ln|5|-3ln|2| is ln(125/8)