What is log_{b}((p^3q^6)/(m^3b^9)) ?

The solution to log_{b}((p^3q^6)/(m^3b^9)) is 3log_{b}(p)+6log_{b}(q)-3log_{b}(m)-9

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simplify log_{b}((p^3q^6)/(m^3b^9))

simplify

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{3} b ^{9}})

3 lo g_{b} (p) + 6 lo g_{b} (q) - 3 lo g_{b} (m) - 9

Solution steps

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{3} b ^{9}})

Apply log rule:

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

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{3} b ^{9}}) = lo g_{b} (p^{3} q^{6}) - lo g_{b} (m^{3} b^{9})

= lo g_{b} (p^{3} q^{6}) - lo g_{b} (m^{3} b^{9})

lo g_{b} (p^{3} q^{6}) = 3 lo g_{b} (p) + 6 lo g_{b} (q)

lo g_{b} (m^{3} b^{9}) = 3 lo g_{b} (m) + 9

= 3 lo g_{b} (p) + 6 lo g_{b} (q) - (3 lo g_{b} (m) + 9)

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{b} (m) + 9) = - 3 lo g_{b} (m) - 9

= 3 lo g_{b} (p) + 6 lo g_{b} (q) - 3 lo g_{b} (m) - 9

lo g_{8} (\frac{5}{x})

16 lo g_{4} (a) - 4 lo g_{4} (b)

lo g_{a} (x^{2} y)

ln (2) 2

What is log_{b}((p^3q^6)/(m^3b^9)) ?
The solution to log_{b}((p^3q^6)/(m^3b^9)) is 3log_{b}(p)+6log_{b}(q)-3log_{b}(m)-9