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Popular >

simplify 2ln(2)+3ln(3)

Solution

simplify

2 ln (2) + 3 ln (3)

Solution

ln (108)

+1

Decimal Notation

4.68213 \dots

Solution steps

2 ln (2) + 3 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (2^{2}) + ln (3^{3}) = ln (3^{3} \cdot 2^{2})

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

2^{2} \cdot 3^{3} = 108

= ln (108)

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Frequently Asked Questions (FAQ)

What is 2ln(2)+3ln(3) ?
The solution to 2ln(2)+3ln(3) is ln(108)