What is 7ln(6/7)-ln(6) ?

The solution to 7ln(6/7)-ln(6) is ln(46656/823543)

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simplify 7ln(6/7)-ln(6)

simplify

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

ln (\frac{46656}{823543})

Decimal

- 2.87081 \dots

Solution steps

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

Apply log rule:

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

7 ln (\frac{6}{7}) = ln ((\frac{6}{7})^{7})

= ln ((\frac{6}{7})^{7}) - ln (6)

Apply log rule:

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

ln ((\frac{6}{7})^{7}) - ln (6) = ln (\frac{( \frac{6}{7} ) ^{7}}{6})

= ln (\frac{( \frac{6}{7} ) ^{7}}{6})

\frac{( \frac{6}{7} ) ^{7}}{6} = \frac{46656}{823543}

= ln (\frac{46656}{823543})

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