What is log_{5}(3)+4log_{5}(y) ?

The solution to log_{5}(3)+4log_{5}(y) is log_{5}(3y^4)

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simplify log_{5}(3)+4log_{5}(y)

simplify

lo g_{5} (3) + 4 lo g_{5} (y)

lo g_{5} (3 y^{4})

Solution steps

lo g_{5} (3) + 4 lo g_{5} (y)

Apply log rule:

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

4 lo g_{5} (y) = lo g_{5} (y^{4})

= lo g_{5} (3) + lo g_{5} (y^{4})

Apply log rule:

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

lo g_{5} (3) + lo g_{5} (y^{4}) = lo g_{5} (3 y^{4})

= lo g_{5} (3 y^{4})

\frac{2}{3} lo g_{10} (2)

6 ln (\frac{36.5}{6})

- 25 lo g_{10} (3) + 25 lo g_{10} (7)

ln (4.4 \cdot 1 0^{9})

10 \cdot lo g_{10} (0.68 \cdot (π \cdot \frac{6.5}{0.0161})^{2})

What is log_{5}(3)+4log_{5}(y) ?
The solution to log_{5}(3)+4log_{5}(y) is log_{5}(3y^4)