What is 12log_{5}(x)-6log_{5}(y) ?

The solution to 12log_{5}(x)-6log_{5}(y) is log_{5}((x^{12})/(y^6))

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simplify 12log_{5}(x)-6log_{5}(y)

simplify

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

lo g_{5} (\frac{x ^{12}}{y ^{6}})

Solution steps

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

Apply log rule:

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

12 lo g_{5} (x) = lo g_{5} (x^{12})

= lo g_{5} (x^{12}) - 6 lo g_{5} (y)

Apply log rule:

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

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

= lo g_{5} (x^{12}) - lo g_{5} (y^{6})

Apply log rule:

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

lo g_{5} (x^{12}) - lo g_{5} (y^{6}) = lo g_{5} (\frac{x ^{12}}{y ^{6}})

= lo g_{5} (\frac{x ^{12}}{y ^{6}})

ln (\frac{2}{24})

- lo g_{10} (4 \cdot 1 0^{- 12})

5 ln (5) + 5 ln (x)

ln (\frac{1}{35})

ln ((2)^{2} (3 - (2)))

What is 12log_{5}(x)-6log_{5}(y) ?
The solution to 12log_{5}(x)-6log_{5}(y) is log_{5}((x^{12})/(y^6))