What is log_{10}(x*y*z^5) ?

The solution to log_{10}(x*y*z^5) is log_{10}(x)+log_{10}(y)+5log_{10}(z)

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simplify log_{10}(xyz^5)

simplify

lo g_{10} (x \cdot y \cdot z^{5})

lo g_{10} (x) + lo g_{10} (y) + 5 lo g_{10} (z)

Solution steps

lo g_{10} (x y z^{5})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (x y z^{5}) = lo g_{10} (x) + lo g_{10} (y) + lo g_{10} (z^{5})

= lo g_{10} (x) + lo g_{10} (y) + lo g_{10} (z^{5})

Simplify

lo g_{10} (z^{5}) : 5 lo g_{10} (z)

= lo g_{10} (x) + lo g_{10} (y) + 5 lo g_{10} (z)

(lo g_{c} (x) - lo g_{c} (y)) + 5 lo g_{c} (v)

1 + lo g_{10} (a) - \frac{1}{2} lo g_{10} (b)

lo g_{10} (\frac{( 100 x ) ^{2}}{27})

3 [ln (x) - 2 ln (x^{2} + 1)] - 2 ln (5)

ln (\frac{x ^{2} y}{z ^{4}})

What is log_{10}(x*y*z^5) ?
The solution to log_{10}(x*y*z^5) is log_{10}(x)+log_{10}(y)+5log_{10}(z)