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

The solution to 4ln(3)-4ln(2) is ln(81/16)

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

simplify

4 ln (3) - 4 ln (2)

ln (\frac{81}{16})

Decimal Notation

1.62186 \dots

Solution steps

4 ln (3) - 4 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{3 ^{4}}{2 ^{4}} = \frac{81}{16}

= ln (\frac{81}{16})

lo g_{10} (\frac{( 2 x ^{2} + 6 )}{( 3 x + 9 )})

ln (\frac{a x + b}{c x + d})

\frac{1}{4} \cdot lo g_{e} (\frac{4}{3})

ln (3) + ln (\frac{3}{- 2} + 1) + \frac{2}{\frac{3}{- 2} + 1}

- lo g_{10} (7.5 \cdot 1 0^{- 11})