What is log_{b}((p^2q^5)/(m^5b^7)) ?

The solution to log_{b}((p^2q^5)/(m^5b^7)) is 2log_{b}(p)+5log_{b}(q)-5log_{b}(m)-7

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simplify log_{b}((p^2q^5)/(m^5b^7))

simplify

lo g_{b} (\frac{p ^{2} q ^{5}}{m ^{5} b ^{7}})

2 lo g_{b} (p) + 5 lo g_{b} (q) - 5 lo g_{b} (m) - 7

Solution steps

lo g_{b} (\frac{p ^{2} q ^{5}}{m ^{5} b ^{7}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{b} (\frac{p ^{2} q ^{5}}{m ^{5} b ^{7}}) = lo g_{b} (p^{2} q^{5}) - lo g_{b} (m^{5} b^{7})

= lo g_{b} (p^{2} q^{5}) - lo g_{b} (m^{5} b^{7})

lo g_{b} (p^{2} q^{5}) = 2 lo g_{b} (p) + 5 lo g_{b} (q)

lo g_{b} (m^{5} b^{7}) = 5 lo g_{b} (m) + 7

= 2 lo g_{b} (p) + 5 lo g_{b} (q) - (5 lo g_{b} (m) + 7)

Apply the distributive law:

- (a + b) = - a - b

- (5 lo g_{b} (m) + 7) = - 5 lo g_{b} (m) - 7

= 2 lo g_{b} (p) + 5 lo g_{b} (q) - 5 lo g_{b} (m) - 7

lo g_{5} (11) - lo g_{5} (9)

\frac{2}{3} lo g_{2} (5)

ln (x^{7} e^{- 2 x^{2}})

lo g_{x} (4 a) + 2 lo g_{x} (a) - 3 lo g_{x} (a)

ln (6 y)

What is log_{b}((p^2q^5)/(m^5b^7)) ?
The solution to log_{b}((p^2q^5)/(m^5b^7)) is 2log_{b}(p)+5log_{b}(q)-5log_{b}(m)-7