What is 6log_{4}(x)-3log_{4}(y) ?

The solution to 6log_{4}(x)-3log_{4}(y) is log_{4}((x^6)/(y^3))

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simplify 6log_{4}(x)-3log_{4}(y)

simplify

6 lo g_{4} (x) - 3 lo g_{4} (y)

lo g_{4} (\frac{x ^{6}}{y ^{3}})

Solution steps

6 lo g_{4} (x) - 3 lo g_{4} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 lo g_{4} (x) = lo g_{4} (x^{6})

= lo g_{4} (x^{6}) - 3 lo g_{4} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{4} (y) = lo g_{4} (y^{3})

= lo g_{4} (x^{6}) - lo g_{4} (y^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{4} (x^{6}) - lo g_{4} (y^{3}) = lo g_{4} (\frac{x ^{6}}{y ^{3}})

= lo g_{4} (\frac{x ^{6}}{y ^{3}})

lo g_{y} (3 ab c)

lo g_{10} (\frac{b ^{3}}{a})

lo g_{10} (m^{n}) - lo g_{10} (p^{q})

- 3 lo g_{5} (\frac{1}{x}) + \frac{1}{2} lo g_{5} (x)

What is 6log_{4}(x)-3log_{4}(y) ?
The solution to 6log_{4}(x)-3log_{4}(y) is log_{4}((x^6)/(y^3))