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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{x ^{5} x + 2}{x + 8})

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

lo g_{10} (\frac{2 x ( 1 - 5 x ) ^{\frac{3}{2}}}{( x + 4 ) ^{3}})

ln (\frac{0.075}{0.06})

ln (\frac{2}{e ^{(- 1)} - e})

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