What is 5log_{6}(x)-3log_{6}(y) ?

The solution to 5log_{6}(x)-3log_{6}(y) is log_{6}((x^5)/(y^3))

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simplify 5log_{6}(x)-3log_{6}(y)

simplify

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

lo g_{6} (\frac{x ^{5}}{y ^{3}})

Solution steps

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

Apply log rule:

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

5 lo g_{6} (x) = lo g_{6} (x^{5})

= lo g_{6} (x^{5}) - 3 lo g_{6} (y)

Apply log rule:

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

3 lo g_{6} (y) = lo g_{6} (y^{3})

= lo g_{6} (x^{5}) - lo g_{6} (y^{3})

Apply log rule:

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

lo g_{6} (x^{5}) - lo g_{6} (y^{3}) = lo g_{6} (\frac{x ^{5}}{y ^{3}})

= lo g_{6} (\frac{x ^{5}}{y ^{3}})

lo g_{10} (\frac{x}{100})

- lo g_{10} (5 \cdot 1 0^{- 5})

lo g_{3} (\frac{x ^{4}}{x + 2})

16.7 + 10 \cdot lo g_{10} (\frac{10400}{120})

What is 5log_{6}(x)-3log_{6}(y) ?
The solution to 5log_{6}(x)-3log_{6}(y) is log_{6}((x^5)/(y^3))