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

The solution to simplify-2ln(3)+3ln(4)+3ln(2) is ln(512/9)

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

simplify

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

ln (\frac{512}{9})

Decimal Notation

4.04110 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{4 ^{3}}{3 ^{2}} = \frac{64}{9}

= ln (\frac{64}{9}) + 3 ln (2)

Apply log rule:

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

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

= ln (\frac{64}{9}) + ln (2^{3})

Apply log rule:

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

ln (\frac{64}{9}) + ln (2^{3}) = ln (2^{3} \cdot \frac{64}{9})

= ln (2^{3} \cdot \frac{64}{9})

\frac{64}{9} \cdot 2^{3} = \frac{512}{9}

= ln (\frac{512}{9})

lo g_{a} (\frac{3}{2})

lo g_{10} (y^{6} z)

lo g_{10} (x + 1) - lo g_{10} (x - 1)

lo g_{10} (\frac{x ^{5}}{z y ^{4}})

What is simplify-2ln(3)+3ln(4)+3ln(2) ?
The solution to simplify-2ln(3)+3ln(4)+3ln(2) is ln(512/9)