What is log_{b}((p^3q^6)/(m^4b^7)) ?

The solution to log_{b}((p^3q^6)/(m^4b^7)) is 3log_{b}(p)+6log_{b}(q)-4log_{b}(m)-7

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simplify log_{b}((p^3q^6)/(m^4b^7))

simplify

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{4} b ^{7}})

3 lo g_{b} (p) + 6 lo g_{b} (q) - 4 lo g_{b} (m) - 7

Solution steps

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{4} 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 ^{4} b ^{7}}) = lo g_{b} (p^{3} q^{6}) - lo g_{b} (m^{4} b^{7})

= lo g_{b} (p^{3} q^{6}) - lo g_{b} (m^{4} b^{7})

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

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

= 3 lo g_{b} (p) + 6 lo g_{b} (q) - (4 lo g_{b} (m) + 7)

Apply the distributive law:

- (a + b) = - a - b

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

= 3 lo g_{b} (p) + 6 lo g_{b} (q) - 4 lo g_{b} (m) - 7

lo g_{10} (3 x + 9) + lo g_{10} (x + 8)

lo g_{b} (x) + lo g_{b} (x + 6) - lo g_{b} (24)

ln (\frac{x - 1}{x})

lo g_{10} (3) + lo g_{10} (x - 8)

2 [ln (x) + \frac{1}{4} ln (x + 9)]

What is log_{b}((p^3q^6)/(m^4b^7)) ?
The solution to log_{b}((p^3q^6)/(m^4b^7)) is 3log_{b}(p)+6log_{b}(q)-4log_{b}(m)-7