What is 5log_{5}(x)-25log_{5}(y) ?

The solution to 5log_{5}(x)-25log_{5}(y) is log_{5}((x^5)/(y^{25)})

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simplify 5log_{5}(x)-25log_{5}(y)

simplify

5 lo g_{5} (x) - 25 lo g_{5} (y)

lo g_{5} (\frac{x ^{5}}{y ^{25}})

Solution steps

5 lo g_{5} (x) - 25 lo g_{5} (y)

Apply log rule:

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

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

= lo g_{5} (x^{5}) - 25 lo g_{5} (y)

Apply log rule:

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

25 lo g_{5} (y) = lo g_{5} (y^{25})

= lo g_{5} (x^{5}) - lo g_{5} (y^{25})

Apply log rule:

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

lo g_{5} (x^{5}) - lo g_{5} (y^{25}) = lo g_{5} (\frac{x ^{5}}{y ^{25}})

= lo g_{5} (\frac{x ^{5}}{y ^{25}})

- \frac{5}{4} ln (\frac{1}{4})

ln (- α (x - θ)^{2}) - ln (2 θ^{2} x)

6 ln (x) + 3 ln (y)

ln (18) + ln (z)

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

What is 5log_{5}(x)-25log_{5}(y) ?
The solution to 5log_{5}(x)-25log_{5}(y) is log_{5}((x^5)/(y^{25)})