What is 6ln(7)-9ln(8) ?

The solution to 6ln(7)-9ln(8) is ln(117649/134217728)

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simplify 6ln(7)-9ln(8)

simplify

6 ln (7) - 9 ln (8)

ln (\frac{117649}{134217728})

Decimal Notation

- 7.03951 \dots

Solution steps

6 ln (7) - 9 ln (8)

Apply log rule:

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

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

= ln (7^{6}) - 9 ln (8)

Apply log rule:

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

9 ln (8) = ln (8^{9})

= ln (7^{6}) - ln (8^{9})

Apply log rule:

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

ln (7^{6}) - ln (8^{9}) = ln (\frac{7 ^{6}}{8 ^{9}})

= ln (\frac{7 ^{6}}{8 ^{9}})

\frac{7 ^{6}}{8 ^{9}} = \frac{117649}{134217728}

= ln (\frac{117649}{134217728})

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