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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

ln (x) - ln (sin (\frac{y}{x}))

- lo g_{10} (1.16 \cdot 1 0^{- 3})

- \frac{1}{3} ln (\frac{7}{4})

lo g_{e} (\frac{1}{2}) + 1

4 lo g_{2} (a) + 6 lo g_{2} (b)

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