What is log_{b}((p^4q^7)/(m^5b^7)) ?

The solution to log_{b}((p^4q^7)/(m^5b^7)) is 4log_{b}(p)+7log_{b}(q)-5log_{b}(m)-7

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simplify log_{b}((p^4q^7)/(m^5b^7))

simplify

lo g_{b} (\frac{p ^{4} q ^{7}}{m ^{5} b ^{7}})

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

Solution steps

lo g_{b} (\frac{p ^{4} q ^{7}}{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 ^{4} q ^{7}}{m ^{5} b ^{7}}) = lo g_{b} (p^{4} q^{7}) - lo g_{b} (m^{5} b^{7})

= lo g_{b} (p^{4} q^{7}) - lo g_{b} (m^{5} b^{7})

lo g_{b} (p^{4} q^{7}) = 4 lo g_{b} (p) + 7 lo g_{b} (q)

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

= 4 lo g_{b} (p) + 7 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

= 4 lo g_{b} (p) + 7 lo g_{b} (q) - 5 lo g_{b} (m) - 7

lo g_{10} (y z^{6})

lo g_{10} (3 x^{2} y)

ln (\frac{23}{0.22})

4 lo g_{10} (x) + lo g_{10} (x^{2}) - lo g_{10} (x^{4})

lo g_{9} (\frac{2 x ^{3}}{3})

What is log_{b}((p^4q^7)/(m^5b^7)) ?
The solution to log_{b}((p^4q^7)/(m^5b^7)) is 4log_{b}(p)+7log_{b}(q)-5log_{b}(m)-7