What is 3ln(4)-4ln(3) ?

The solution to 3ln(4)-4ln(3) is ln(64/81)

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simplify 3ln(4)-4ln(3)

simplify

3 ln (4) - 4 ln (3)

ln (\frac{64}{81})

Decimal Notation

- 0.23556 \dots

Solution steps

3 ln (4) - 4 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{4 ^{3}}{3 ^{4}} = \frac{64}{81}

= ln (\frac{64}{81})

ln (x) - [ln (x + 1) + ln (x - 1)]

lo g_{b} (x) + lo g_{b} (y) - lo g_{b} (u)

\frac{1}{2} lo g_{b} (x) + 5 lo g_{b} (y) - 4 lo g_{b} (x)

lo g_{3} (x y)

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