What is ln((p^6q^7)/(4\sqrt[6]{r)}) ?

The solution to ln((p^6q^7)/(4\sqrt[6]{r)}) is 6ln(p)+7ln(q)-2ln(2)-ln(\sqrt[6]{r})

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simplify ln((p^6q^7)/(4\sqrt[6]{r)})

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

Apply log rule:

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

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

Apply log rule:

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

ln (q^{7}) = 7 ln (q)

ln (4) = 2 ln (2)

ln (b e^{m t})

ln (\frac{K ^{\frac{3}{4}} L}{K + 1})

ln (\frac{c}{2}) - ln (x)

2 lo g_{5} (- 6 lo g_{5} (y))

ln (\frac{1}{1 - e ^{- x}} e^{- x})

What is ln((p^6q^7)/(4\sqrt[6]{r)}) ?
The solution to ln((p^6q^7)/(4\sqrt[6]{r)}) is 6ln(p)+7ln(q)-2ln(2)-ln(\sqrt[6]{r})