What is 6ln(6)-4ln(4)-2 ?

The solution to 6ln(6)-4ln(4)-2 is ln(729/4)-2

Popular >

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

simplify

6 ln (6) - 4 ln (4) - 2

ln (\frac{729}{4}) - 2

Decimal Notation

3.20537 \dots

Solution steps

6 ln (6) - 4 ln (4) - 2

Apply log rule:

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

6 ln (6) = ln (6^{6})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{6 ^{6}}{4 ^{4}} = \frac{729}{4}

= ln (\frac{729}{4}) - 2

ln (\frac{0.1}{0.9})

\frac{1}{2 a} (ln \frac{u}{a} + 1 - ln \frac{u}{a} - 1) + C

ln (x (y + 1))

ln (- \frac{4}{3}) - ln (- \frac{7}{6})

ln (2 x) + ln (3 x)