What is log_{b}((ay^5)/(m^3n^4)) ?

The solution to log_{b}((ay^5)/(m^3n^4)) is log_{b}(a)+5log_{b}(y)-3log_{b}(m)-4log_{b}(n)

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simplify log_{b}((ay^5)/(m^3n^4))

simplify

lo g_{b} (\frac{a y ^{5}}{m ^{3} n ^{4}})

lo g_{b} (a) + 5 lo g_{b} (y) - 3 lo g_{b} (m) - 4 lo g_{b} (n)

Solution steps

lo g_{b} (\frac{a y ^{5}}{m ^{3} n ^{4}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{b} (\frac{a y ^{5}}{m ^{3} n ^{4}}) = lo g_{b} (a y^{5}) - lo g_{b} (m^{3} n^{4})

= lo g_{b} (a y^{5}) - lo g_{b} (m^{3} n^{4})

lo g_{b} (a y^{5}) = lo g_{b} (a) + 5 lo g_{b} (y)

lo g_{b} (m^{3} n^{4}) = 3 lo g_{b} (m) + 4 lo g_{b} (n)

= lo g_{b} (a) + 5 lo g_{b} (y) - (3 lo g_{b} (m) + 4 lo g_{b} (n))

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{b} (m) + 4 lo g_{b} (n)) = - 3 lo g_{b} (m) - 4 lo g_{b} (n)

= lo g_{b} (a) + 5 lo g_{b} (y) - 3 lo g_{b} (m) - 4 lo g_{b} (n)

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

\frac{1}{3} lo g_{10} (3)

lo g_{10} (z^{3} y)

ln (a) - ln (b) + ln (c)

lo g_{8} (\frac{x ^{4}}{y})

What is log_{b}((ay^5)/(m^3n^4)) ?
The solution to log_{b}((ay^5)/(m^3n^4)) is log_{b}(a)+5log_{b}(y)-3log_{b}(m)-4log_{b}(n)