What is 3log_{5}(x)+log_{5}(y) ?

The solution to 3log_{5}(x)+log_{5}(y) is log_{5}(x^3y)

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simplify 3log_{5}(x)+log_{5}(y)

simplify

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

lo g_{5} (x^{3} y)

Solution steps

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

Apply log rule:

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

3 lo g_{5} (x) = lo g_{5} (x^{3})

= lo g_{5} (x^{3}) + lo g_{5} (y)

Apply log rule:

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

lo g_{5} (x^{3}) + lo g_{5} (y) = lo g_{5} (x^{3} y)

= lo g_{5} (x^{3} y)

- lo g_{10} (2.6 \cdot 1 0^{- 6})

\frac{1}{4} ln (\frac{11}{7})

3 lo g_{10} (a) - 2 lo g_{10} (k)

2 lo g_{10} (x) + \frac{1}{2} lo g_{10} (y)

ln (7) - 2 ln (2)

What is 3log_{5}(x)+log_{5}(y) ?
The solution to 3log_{5}(x)+log_{5}(y) is log_{5}(x^3y)