What is ln((12!)/(7!*5!))-ln(11) ?

The solution to ln((12!)/(7!*5!))-ln(11) is ln(72)

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simplify ln((12!)/(7!*5!))-ln(11)

simplify

ln (\frac{12 !}{7 ! \cdot 5 !}) - ln (11)

ln (72)

Decimal Notation

4.27666 \dots

Solution steps

ln (\frac{12 !}{7 ! \cdot 5 !}) - ln (11)

Apply log rule:

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

ln (\frac{12 !}{7 ! \cdot 5 !}) - ln (11) = ln (\frac{\frac{12 !}{7 ! \cdot 5 !}}{11})

= ln (\frac{\frac{12 !}{7 ! \cdot 5 !}}{11})

\frac{\frac{12 !}{7 ! \cdot 5 !}}{11} = 72

= ln (72)

lo g_{10} (\frac{136.93}{10}) - 110

ln (\frac{250000000}{160141})

2 lo g_{3} (z) + 3 (lo g_{3} (w) - 2 lo g_{3} (y))

(0.0256) \cdot ln (\frac{( 5 \cdot 1 0 ^{15} )}{1.5 \cdot 1 0 ^{10}})

- ln (cos (x)) - ln (x)

What is ln((12!)/(7!*5!))-ln(11) ?
The solution to ln((12!)/(7!*5!))-ln(11) is ln(72)