What is 6log_{5}(x)-36log_{5}(y) ?

The solution to 6log_{5}(x)-36log_{5}(y) is log_{5}((x^6)/(y^{36)})

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simplify 6log_{5}(x)-36log_{5}(y)

simplify

6 lo g_{5} (x) - 36 lo g_{5} (y)

lo g_{5} (\frac{x ^{6}}{y ^{36}})

Solution steps

6 lo g_{5} (x) - 36 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}) - 36 lo g_{5} (y)

Apply log rule:

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

36 lo g_{5} (y) = lo g_{5} (y^{36})

= lo g_{5} (x^{6}) - lo g_{5} (y^{36})

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^{36}) = lo g_{5} (\frac{x ^{6}}{y ^{36}})

= lo g_{5} (\frac{x ^{6}}{y ^{36}})

lo g_{4} (\frac{\frac{x}{z}}{w})

ln (24) - ln (8)

ln (\frac{2 x}{3})

lo g_{2} ((a^{5} b^{2})^{3})

1000 e^{\frac{4 l n ( 2 )}{3}}

What is 6log_{5}(x)-36log_{5}(y) ?
The solution to 6log_{5}(x)-36log_{5}(y) is log_{5}((x^6)/(y^{36)})