What is log_{10}(x)+4log_{10}(y)-5log_{10}(z) ?

The solution to log_{10}(x)+4log_{10}(y)-5log_{10}(z) is log_{10}((xy^4)/(z^5))

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simplify log_{10}(x)+4log_{10}(y)-5log_{10}(z)

simplify

lo g_{10} (x) + 4 lo g_{10} (y) - 5 lo g_{10} (z)

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

Solution steps

lo g_{10} (x) + 4 lo g_{10} (y) - 5 lo g_{10} (z)

Apply log rule:

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

4 lo g_{10} (y) = lo g_{10} (y^{4})

= lo g_{10} (x) + lo g_{10} (y^{4}) - 5 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x) + lo g_{10} (y^{4}) = lo g_{10} (x y^{4})

= lo g_{10} (x y^{4}) - 5 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x y^{4}) - lo g_{10} (z^{5})

Apply log rule:

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

lo g_{10} (x y^{4}) - lo g_{10} (z^{5}) = lo g_{10} (\frac{x y ^{4}}{z ^{5}})

= lo g_{10} (\frac{x y ^{4}}{z ^{5}})

ln (\frac{e ^{5}}{7})

ln (3) - ln (5)

- \frac{4}{5} lo g_{2} (\frac{4}{5}) - \frac{1}{5} lo g_{2} (\frac{1}{5})

ln (x x^{2} + y^{2})

lo g_{4} (3) + lo g_{4} (7)

What is log_{10}(x)+4log_{10}(y)-5log_{10}(z) ?
The solution to log_{10}(x)+4log_{10}(y)-5log_{10}(z) is log_{10}((xy^4)/(z^5))