What is 6+2ln(6)-2ln(20/3) ?

The solution to 6+2ln(6)-2ln(20/3) is 6+ln(81/100)

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simplify 6+2ln(6)-2ln(20/3)

simplify

6 + 2 ln (6) - 2 ln (\frac{20}{3})

6 + ln (\frac{81}{100})

Decimal Notation

5.78927 \dots

Solution steps

6 + 2 ln (6) - 2 ln (\frac{20}{3})

Apply log rule:

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

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

= 6 + ln (6^{2}) - 2 ln (\frac{20}{3})

Apply log rule:

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

2 ln (\frac{20}{3}) = ln ((\frac{20}{3})^{2})

= 6 + ln (6^{2}) - ln ((\frac{20}{3})^{2})

Apply log rule:

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

ln (6^{2}) - ln ((\frac{20}{3})^{2}) = ln (\frac{6 ^{2}}{( \frac{20}{3} ) ^{2}})

= 6 + ln (\frac{6 ^{2}}{( \frac{20}{3} ) ^{2}})

\frac{6 ^{2}}{( \frac{20}{3} ) ^{2}} = \frac{81}{100}

= 6 + ln (\frac{81}{100})

lo g_{10} (\frac{12.8}{5.76})

ln (\frac{e ^{c}}{( x + 1 ) ^{2}})

ln (\frac{λ ^{x} e ^{- λ}}{x !})

ln (\frac{ln ( x )}{sin ( x )})

ln (r) - \frac{1}{2} ln (r^{2} + 1)