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

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

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

expand

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 (x^{y} \cdot (1 - x)^{z - y})

0.0259 \cdot ln (\frac{4.7 \cdot 1 0 ^{17}}{1.15 \cdot 1 0 ^{14}})

ln (40) - ln (4)

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

- 450 ln (\frac{c}{1.75 b})

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