What is ln((2^4)/(3^25^{-4)}) ?

The solution to ln((2^4)/(3^25^{-4)}) is 4ln(2)-2ln(3)+4ln(5)

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simplify ln((2^4)/(3^25^{-4)})

simplify

ln (\frac{2 ^{4}}{3 ^{2} 5 ^{- 4}})

4 ln (2) - 2 ln (3) + 4 ln (5)

Decimal Notation

7.01311 \dots

Solution steps

ln (\frac{2 ^{4}}{3 ^{2} \cdot 5 ^{- 4}})

Apply log rule:

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

ln (\frac{2 ^{4}}{3 ^{2} \cdot 5 ^{- 4}}) = ln (2^{4}) - ln (3^{2} \cdot 5^{- 4})

= ln (2^{4}) - ln (5^{- 4} \cdot 3^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{4}) = 4 ln (2)

= 4 ln (2) - ln (3^{2} \cdot 5^{- 4})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (3^{2} \cdot 5^{- 4}) = ln (3^{2}) + ln (5^{- 4})

= 4 ln (2) - (ln (3^{2}) + ln (5^{- 4}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (3^{2}) = 2 ln (3)

= 4 ln (2) - (2 ln (3) + ln (5^{- 4}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (5^{- 4}) = - 4 ln (5)

= 4 ln (2) - (2 ln (3) - 4 ln (5))

- (2 ln (3) - 4 ln (5)) : - 2 ln (3) + 4 ln (5)

= 4 ln (2) - 2 ln (3) + 4 ln (5)

ln (8 x) - ln (2 x)

ln (\frac{1}{( r - 1 ) !} θ^{- w} x^{w - 1} e^{- x θ^{- 1}})

- \frac{1}{2} ln (\frac{1}{2}) + \frac{1}{2}

lo g_{6} (2 x) - lo g_{6} (x - 3) 3

\frac{24}{π} ln (2 + 3)

What is ln((2^4)/(3^25^{-4)}) ?
The solution to ln((2^4)/(3^25^{-4)}) is 4ln(2)-2ln(3)+4ln(5)