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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

lo g_{5} (x y^{2})

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

ln (1200 - y) + ln (y - 100)

\frac{2 ln ( 3 )}{ln ( 2 ) - ln ( 3 )}

lo g_{e} (4 x y)

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