What is 25log_{6}(x)+5log_{6}(y) ?

The solution to 25log_{6}(x)+5log_{6}(y) is log_{6}(x^{25}y^5)

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simplify 25log_{6}(x)+5log_{6}(y)

simplify

25 lo g_{6} (x) + 5 lo g_{6} (y)

lo g_{6} (x^{25} y^{5})

Solution steps

25 lo g_{6} (x) + 5 lo g_{6} (y)

Apply log rule:

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

25 lo g_{6} (x) = lo g_{6} (x^{25})

= lo g_{6} (x^{25}) + 5 lo g_{6} (y)

Apply log rule:

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

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

= lo g_{6} (x^{25}) + lo g_{6} (y^{5})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{6} (x^{25}) + lo g_{6} (y^{5}) = lo g_{6} (x^{25} y^{5})

= lo g_{6} (x^{25} y^{5})

- ln (\frac{2}{5})

3 (lo g_{5} (x) + 3 lo g_{5} (y) - 5 lo g_{5} (z))

lo g_{5} (x^{2})

lo g_{e} (\frac{7}{2})

\frac{9}{4} ln (\frac{9}{4})

What is 25log_{6}(x)+5log_{6}(y) ?
The solution to 25log_{6}(x)+5log_{6}(y) is log_{6}(x^{25}y^5)