What is 10log_{6}(x)-2log_{6}(y) ?

The solution to 10log_{6}(x)-2log_{6}(y) is log_{6}((x^{10})/(y^2))

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simplify 10log_{6}(x)-2log_{6}(y)

simplify

10 lo g_{6} (x) - 2 lo g_{6} (y)

lo g_{6} (\frac{x ^{10}}{y ^{2}})

Solution steps

10 lo g_{6} (x) - 2 lo g_{6} (y)

Apply log rule:

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

10 lo g_{6} (x) = lo g_{6} (x^{10})

= lo g_{6} (x^{10}) - 2 lo g_{6} (y)

Apply log rule:

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

2 lo g_{6} (y) = lo g_{6} (y^{2})

= lo g_{6} (x^{10}) - lo g_{6} (y^{2})

Apply log rule:

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

lo g_{6} (x^{10}) - lo g_{6} (y^{2}) = lo g_{6} (\frac{x ^{10}}{y ^{2}})

= lo g_{6} (\frac{x ^{10}}{y ^{2}})

lo g_{10} (23 pq)

lo g_{b} (\frac{32}{125})

- 5 ln (x) - 9 ln (y) + \frac{1}{9} ln (z)

lo g_{10} (\frac{z ^{3}}{x ^{2} y ^{5}})

- ln \frac{8}{3} + \frac{8}{3} (0) + ln \frac{2}{3} + \frac{8}{3} (0)

What is 10log_{6}(x)-2log_{6}(y) ?
The solution to 10log_{6}(x)-2log_{6}(y) is log_{6}((x^{10})/(y^2))