What is log_{b}((p^4q^5)/(m^3b^9)) ?

The solution to log_{b}((p^4q^5)/(m^3b^9)) is 4log_{b}(p)+5log_{b}(q)-3log_{b}(m)-9

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simplify log_{b}((p^4q^5)/(m^3b^9))

simplify

lo g_{b} (\frac{p ^{4} q ^{5}}{m ^{3} b ^{9}})

4 lo g_{b} (p) + 5 lo g_{b} (q) - 3 lo g_{b} (m) - 9

Solution steps

lo g_{b} (\frac{p ^{4} q ^{5}}{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 ^{4} q ^{5}}{m ^{3} b ^{9}}) = lo g_{b} (p^{4} q^{5}) - lo g_{b} (m^{3} b^{9})

= lo g_{b} (p^{4} q^{5}) - lo g_{b} (m^{3} b^{9})

lo g_{b} (p^{4} q^{5}) = 4 lo g_{b} (p) + 5 lo g_{b} (q)

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

= 4 lo g_{b} (p) + 5 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

= 4 lo g_{b} (p) + 5 lo g_{b} (q) - 3 lo g_{b} (m) - 9

lo g_{3} (\frac{9}{x + 9})

4 lo g_{10} (x) - 2 lo g_{10} (y) + 3 lo g_{10} (z)

\frac{1}{3} (lo g_{8} (a) + 2 lo g_{8} (b))

ln (\frac{( 1.6 \cdot 1 0 ^{- 19} )}{( 6.48 \cdot 1 0 ^{- 5} )})

lo g_{10} (2) + \frac{1}{2} \cdot lo g_{10} (15) - \frac{1}{4} \cdot lo g_{10} (9)

What is log_{b}((p^4q^5)/(m^3b^9)) ?
The solution to log_{b}((p^4q^5)/(m^3b^9)) is 4log_{b}(p)+5log_{b}(q)-3log_{b}(m)-9