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Popular >

simplify 5ln(2)+2ln(3)-3ln(4)

Solution

simplify

5 ln (2) + 2 ln (3) - 3 ln (4)

Solution

ln (\frac{9}{2})

+1

Decimal Notation

1.50407 \dots

Solution steps

5 ln (2) + 2 ln (3) - 3 ln (4)

Apply log rule:

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

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

= ln (2^{5}) + 2 ln (3) - 3 ln (4)

Apply log rule:

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

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

= ln (2^{5}) + ln (3^{2}) - 3 ln (4)

Apply log rule:

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

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

= ln (2^{5} \cdot 3^{2}) - 3 ln (4)

2^{5} \cdot 3^{2} = 288

= ln (288) - 3 ln (4)

Apply log rule:

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

3 ln (4) = ln (4^{3})

= ln (288) - ln (4^{3})

Apply log rule:

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

ln (288) - ln (4^{3}) = ln (\frac{288}{4 ^{3}})

= ln (\frac{288}{4 ^{3}})

\frac{288}{4 ^{3}} = \frac{9}{2}

= ln (\frac{9}{2})

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Frequently Asked Questions (FAQ)

What is 5ln(2)+2ln(3)-3ln(4) ?
The solution to 5ln(2)+2ln(3)-3ln(4) is ln(9/2)