What is log_{5}(x)+4log_{5}(y)-2log_{5}(z) ?

The solution to log_{5}(x)+4log_{5}(y)-2log_{5}(z) is log_{5}((xy^4)/(z^2))

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simplify log_{5}(x)+4log_{5}(y)-2log_{5}(z)

simplify

lo g_{5} (x) + 4 lo g_{5} (y) - 2 lo g_{5} (z)

lo g_{5} (\frac{x y ^{4}}{z ^{2}})

Solution steps

lo g_{5} (x) + 4 lo g_{5} (y) - 2 lo g_{5} (z)

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} (x) + lo g_{5} (y^{4}) - 2 lo g_{5} (z)

Apply log rule:

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

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

= lo g_{5} (x y^{4}) - 2 lo g_{5} (z)

Apply log rule:

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

2 lo g_{5} (z) = lo g_{5} (z^{2})

= lo g_{5} (x y^{4}) - lo g_{5} (z^{2})

Apply log rule:

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

lo g_{5} (x y^{4}) - lo g_{5} (z^{2}) = lo g_{5} (\frac{x y ^{4}}{z ^{2}})

= lo g_{5} (\frac{x y ^{4}}{z ^{2}})

\frac{13}{2} ln (26)

ln (\frac{2290000}{130000})

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

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

ln (2 \cdot 2)

What is log_{5}(x)+4log_{5}(y)-2log_{5}(z) ?
The solution to log_{5}(x)+4log_{5}(y)-2log_{5}(z) is log_{5}((xy^4)/(z^2))