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Popular >

simplify 3ln(2)-ln(20)+2ln(5)

Solution

simplify

3 ln (2) - ln (20) + 2 ln (5)

Solution

ln (10)

+1

Decimal Notation

2.30258 \dots

Solution steps

3 ln (2) - ln (20) + 2 ln (5)

Apply log rule:

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

3 ln (2) = ln (2^{3})

= ln (2^{3}) - ln (20) + 2 ln (5)

Apply log rule:

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

ln (2^{3}) - ln (20) = ln (\frac{2 ^{3}}{20})

= ln (\frac{2 ^{3}}{20}) + 2 ln (5)

\frac{2 ^{3}}{20} = \frac{2}{5}

= ln (\frac{2}{5}) + 2 ln (5)

Apply log rule:

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

2 ln (5) = ln (5^{2})

= ln (\frac{2}{5}) + ln (5^{2})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{2}{5}) + ln (5^{2}) = ln (5^{2} \cdot \frac{2}{5})

= ln (5^{2} \cdot \frac{2}{5})

\frac{2}{5} \cdot 5^{2} = 10

= ln (10)

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Frequently Asked Questions (FAQ)

What is 3ln(2)-ln(20)+2ln(5) ?
The solution to 3ln(2)-ln(20)+2ln(5) is ln(10)