What is log_{b}((p^2q^5)/(m^4b^9)) ?

The solution to log_{b}((p^2q^5)/(m^4b^9)) is 2log_{b}(p)+5log_{b}(q)-4log_{b}(m)-9

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simplify log_{b}((p^2q^5)/(m^4b^9))

simplify

lo g_{b} (\frac{p ^{2} q ^{5}}{m ^{4} b ^{9}})

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

Solution steps

lo g_{b} (\frac{p ^{2} q ^{5}}{m ^{4} b ^{9}})

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 ^{4} b ^{9}}) = lo g_{b} (p^{2} q^{5}) - lo g_{b} (m^{4} b^{9})

= lo g_{b} (p^{2} q^{5}) - lo g_{b} (m^{4} b^{9})

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

lo g_{b} (m^{4} b^{9}) = 4 lo g_{b} (m) + 9

= 2 lo g_{b} (p) + 5 lo g_{b} (q) - (4 lo g_{b} (m) + 9)

Apply the distributive law:

- (a + b) = - a - b

- (4 lo g_{b} (m) + 9) = - 4 lo g_{b} (m) - 9

= 2 lo g_{b} (p) + 5 lo g_{b} (q) - 4 lo g_{b} (m) - 9

lo g_{2} (I n e^{4})

ln (\frac{x}{x \cdot y ^{3}})

ln (x^{r}) + ln (y^{r})

3 ln (2 x)

4 ln (\frac{2}{23})

What is log_{b}((p^2q^5)/(m^4b^9)) ?
The solution to log_{b}((p^2q^5)/(m^4b^9)) is 2log_{b}(p)+5log_{b}(q)-4log_{b}(m)-9