What is 5log_{10}(x)+log_{10}(y)-3log_{10}(z) ?

The solution to 5log_{10}(x)+log_{10}(y)-3log_{10}(z) is log_{10}((x^5y)/(z^3))

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simplify 5log_{10}(x)+log_{10}(y)-3log_{10}(z)

simplify

5 lo g_{10} (x) + lo g_{10} (y) - 3 lo g_{10} (z)

lo g_{10} (\frac{x ^{5} y}{z ^{3}})

Solution steps

5 lo g_{10} (x) + lo g_{10} (y) - 3 lo g_{10} (z)

Apply log rule:

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

5 lo g_{10} (x) = lo g_{10} (x^{5})

= lo g_{10} (x^{5}) + lo g_{10} (y) - 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{5} y) - 3 lo g_{10} (z)

Apply log rule:

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

3 lo g_{10} (z) = lo g_{10} (z^{3})

= lo g_{10} (x^{5} y) - lo g_{10} (z^{3})

Apply log rule:

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

lo g_{10} (x^{5} y) - lo g_{10} (z^{3}) = lo g_{10} (\frac{x ^{5} y}{z ^{3}})

= lo g_{10} (\frac{x ^{5} y}{z ^{3}})

ln (\frac{75}{36})

ln (\frac{2}{4})

ln (∣ x ∣ (x^{2} + 4)^{2}) + C

- lo g_{10} (2.6 \cdot 1 0^{- 2})

lo g_{e} (\frac{9}{10})

What is 5log_{10}(x)+log_{10}(y)-3log_{10}(z) ?
The solution to 5log_{10}(x)+log_{10}(y)-3log_{10}(z) is log_{10}((x^5y)/(z^3))