What is expand log_{2}((-3m^2n^4)/(4p)) ?

The solution to expand log_{2}((-3m^2n^4)/(4p)) is log_{2}(3)+2log_{2}(m)+4log_{2}(n)-2-log_{2}(p)

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expand log_{2}((-3m^2n^4)/(4p))

expand

lo g_{2} (\frac{- 3 m ^{2} n ^{4}}{4 p})

lo g_{2} (3) + 2 lo g_{2} (m) + 4 lo g_{2} (n) - 2 - lo g_{2} (p)

Solution steps

lo g_{2} (\frac{- 3 m ^{2} n ^{4}}{4 p})

Apply log rule:

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

lo g_{2} (\frac{- 3 m ^{2} n ^{4}}{4 p}) = lo g_{2} (- 3 m^{2} n^{4}) - lo g_{2} (4 p)

= lo g_{2} (- 3 m^{2} n^{4}) - lo g_{2} (4 p)

Apply log rule:

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

lo g_{2} (- 3 m^{2} n^{4}) = lo g_{2} (3) + lo g_{2} (m^{2}) + lo g_{2} (n^{4}), lo g_{2} (4 p) = lo g_{2} (4) + lo g_{2} (p)

= lo g_{2} (3) + lo g_{2} (m^{2}) + lo g_{2} (n^{4}) - (lo g_{2} (p) + lo g_{2} (4))

Apply log rule:

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

lo g_{2} (m^{2}) = 2 lo g_{2} (m)

= lo g_{2} (3) + 2 lo g_{2} (m) + lo g_{2} (n^{4}) - (lo g_{2} (4) + lo g_{2} (p))

Apply log rule:

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

lo g_{2} (n^{4}) = 4 lo g_{2} (n)

= lo g_{2} (3) + 2 lo g_{2} (m) + 4 lo g_{2} (n) - (lo g_{2} (4) + lo g_{2} (p))

lo g_{2} (4) = 2

= lo g_{2} (3) + 2 lo g_{2} (m) + 4 lo g_{2} (n) - (lo g_{2} (p) + 2)

- (2 + lo g_{2} (p)) : - 2 - lo g_{2} (p)

= lo g_{2} (3) + 2 lo g_{2} (m) + 4 lo g_{2} (n) - 2 - lo g_{2} (p)

lo g_{3} (\frac{27}{x + 2})

ln (5) + 5 ln (3)

\frac{1}{2} (lo g_{5} (x^{6}) + lo g_{5} (x^{3}))

lo g_{a} (\frac{x ^{7}}{y z ^{8}})

What is expand log_{2}((-3m^2n^4)/(4p)) ?
The solution to expand log_{2}((-3m^2n^4)/(4p)) is log_{2}(3)+2log_{2}(m)+4log_{2}(n)-2-log_{2}(p)