What is 25ln(25)-16ln(16)-9ln(e) ?

The solution to 25ln(25)-16ln(16)-9ln(e) is ln((25^{25})/(16^{16)})-9

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simplify 25ln(25)-16ln(16)-9ln(e)

simplify

25 ln (25) - 16 ln (16) - 9 ln (e)

ln (\frac{2 5 ^{25}}{1 6 ^{16}}) - 9

Decimal Notation

27.11047 \dots

Solution steps

25 ln (25) - 16 ln (16) - 9 ln (e)

Apply log rule:

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

25 ln (25) = ln (2 5^{25})

= ln (2 5^{25}) - 16 ln (16) - 9 ln (e)

Apply log rule:

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

16 ln (16) = ln (1 6^{16})

= ln (2 5^{25}) - ln (1 6^{16}) - 9 ln (e)

Apply log rule:

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

ln (2 5^{25}) - ln (1 6^{16}) = ln (\frac{2 5 ^{25}}{1 6 ^{16}})

= ln (\frac{2 5 ^{25}}{1 6 ^{16}}) - 9 ln (e)

9 ln (e) = 9

= ln (\frac{2 5 ^{25}}{1 6 ^{16}}) - 9

ln (\frac{2}{16})

lo g_{10} (\frac{8}{3 ^{2}})

- ln (x) + ln^{2} (x)

ln (\frac{x - y}{x ^{2} + y ^{2}})

ln (\frac{tan ^{5} ( x )}{e ^{6 x^{4}} x ^{6}})

What is 25ln(25)-16ln(16)-9ln(e) ?
The solution to 25ln(25)-16ln(16)-9ln(e) is ln((25^{25})/(16^{16)})-9