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Popular >

simplify 2ln(4)-ln(6)+3ln(2)

Solution

simplify

2 ln (4) - ln (6) + 3 ln (2)

Solution

ln (\frac{64}{3})

+1

Decimal Notation

3.06027 \dots

Solution steps

2 ln (4) - ln (6) + 3 ln (2)

Apply log rule:

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

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

= ln (4^{2}) - ln (6) + 3 ln (2)

Apply log rule:

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

ln (4^{2}) - ln (6) = ln (\frac{4 ^{2}}{6})

= ln (\frac{4 ^{2}}{6}) + 3 ln (2)

\frac{4 ^{2}}{6} = \frac{8}{3}

= ln (\frac{8}{3}) + 3 ln (2)

Apply log rule:

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

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

= ln (\frac{8}{3}) + ln (2^{3})

Apply log rule:

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

ln (\frac{8}{3}) + ln (2^{3}) = ln (2^{3} \cdot \frac{8}{3})

= ln (2^{3} \cdot \frac{8}{3})

\frac{8}{3} \cdot 2^{3} = \frac{64}{3}

= ln (\frac{64}{3})

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Frequently Asked Questions (FAQ)

What is 2ln(4)-ln(6)+3ln(2) ?
The solution to 2ln(4)-ln(6)+3ln(2) is ln(64/3)