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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

ln (\frac{3 x - 5}{2 x - 1})

(\frac{1}{2} ln ∣ 2 (10) + 1 ∣ + 2 ln ∣ 10 - 1 ∣) - 5

ln (\frac{( 1 + 10 x )}{x})

ln (I) - ln (I - N)

\frac{1}{15} ln (\frac{5}{8})

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