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Popular >

simplify 6ln(6)-5ln(5)

Solution

simplify

6 ln (6) - 5 ln (5)

Solution

ln (\frac{46656}{3125})

+1

Decimal Notation

2.70336 \dots

Solution steps

6 ln (6) - 5 ln (5)

Apply log rule:

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

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

= ln (6^{6}) - 5 ln (5)

Apply log rule:

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

5 ln (5) = ln (5^{5})

= ln (6^{6}) - ln (5^{5})

Apply log rule:

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

ln (6^{6}) - ln (5^{5}) = ln (\frac{6 ^{6}}{5 ^{5}})

= ln (\frac{6 ^{6}}{5 ^{5}})

\frac{6 ^{6}}{5 ^{5}} = \frac{46656}{3125}

= ln (\frac{46656}{3125})

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Frequently Asked Questions (FAQ)

What is 6ln(6)-5ln(5) ?
The solution to 6ln(6)-5ln(5) is ln(46656/3125)