What is 6ln(9)-4ln(4)-4 ?

The solution to 6ln(9)-4ln(4)-4 is ln(531441/256)-4

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simplify 6ln(9)-4ln(4)-4

simplify

6 ln (9) - 4 ln (4) - 4

ln (\frac{531441}{256}) - 4

Solution steps

6 ln (9) - 4 ln (4) - 4

Apply log rule:

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

6 ln (9) = ln (9^{6})

= ln (9^{6}) - 4 ln (4) - 4

Apply log rule:

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

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

= ln (9^{6}) - ln (4^{4}) - 4

Apply log rule:

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

ln (9^{6}) - ln (4^{4}) = ln (\frac{9 ^{6}}{4 ^{4}})

= ln (\frac{9 ^{6}}{4 ^{4}}) - 4

\frac{9 ^{6}}{4 ^{4}} = \frac{531441}{256}

= ln (\frac{531441}{256}) - 4

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