What is simplify-3ln(3)+2ln(4) ?

The solution to simplify-3ln(3)+2ln(4) is ln(16/27)

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

simplify

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

ln (\frac{16}{27})

Decimal Notation

- 0.52324 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

2 ln (4) = ln (4^{2})

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

Apply log rule:

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

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

= ln (\frac{4 ^{2}}{3 ^{3}})

\frac{4 ^{2}}{3 ^{3}} = \frac{16}{27}

= ln (\frac{16}{27})

- \frac{1}{6} ln ∣ 5 - 6 (7) ∣ - 3 ln ∣ 7 ∣

lo g_{4} ((x y^{2})^{2})

2 lo g_{6} (y) - \frac{1}{2} lo g_{6} (x) + 4 lo g_{6} (w)

lo g_{6} (\frac{( x + 3 ) ^{2}}{3 y ^{3}})

What is simplify-3ln(3)+2ln(4) ?
The solution to simplify-3ln(3)+2ln(4) is ln(16/27)