What is log_{b}((p^3q^6)/(m^5b^7)) ?

The solution to log_{b}((p^3q^6)/(m^5b^7)) is 3log_{b}(p)+6log_{b}(q)-5log_{b}(m)-7

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simplify log_{b}((p^3q^6)/(m^5b^7))

simplify

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{5} b ^{7}})

3 lo g_{b} (p) + 6 lo g_{b} (q) - 5 lo g_{b} (m) - 7

Solution steps

lo g_{b} (\frac{p ^{3} q ^{6}}{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 ^{3} q ^{6}}{m ^{5} b ^{7}}) = lo g_{b} (p^{3} q^{6}) - lo g_{b} (m^{5} b^{7})

= lo g_{b} (p^{3} q^{6}) - lo g_{b} (m^{5} b^{7})

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

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

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

= 3 lo g_{b} (p) + 6 lo g_{b} (q) - 5 lo g_{b} (m) - 7

7 lo g_{b} (x) + 5 lo g_{b} (z)

lo g_{a} (\frac{1}{2})

lo g_{4} (3) - lo g_{4} (t)

\frac{1}{2} lo g_{a} (x) + 3 lo g_{a} (y) - 3 lo g_{a} (x)

ln (12) - ln (3)

What is log_{b}((p^3q^6)/(m^5b^7)) ?
The solution to log_{b}((p^3q^6)/(m^5b^7)) is 3log_{b}(p)+6log_{b}(q)-5log_{b}(m)-7