What is log_{10}(x)+log_{10}(y)-2log_{10}(z) ?

The solution to log_{10}(x)+log_{10}(y)-2log_{10}(z) is log_{10}((xy)/(z^2))

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simplify log_{10}(x)+log_{10}(y)-2log_{10}(z)

simplify

lo g_{10} (x) + lo g_{10} (y) - 2 lo g_{10} (z)

lo g_{10} (\frac{x y}{z ^{2}})

Solution steps

lo g_{10} (x) + lo g_{10} (y) - 2 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) = lo g_{10} (x y)

= lo g_{10} (x y) - 2 lo g_{10} (z)

Apply log rule:

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

2 lo g_{10} (z) = lo g_{10} (z^{2})

= lo g_{10} (x y) - lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (x y) - lo g_{10} (z^{2}) = lo g_{10} (\frac{x y}{z ^{2}})

= lo g_{10} (\frac{x y}{z ^{2}})

ln (\frac{( x + 2 ) ^{4} y ^{\frac{1}{3}}}{( w - 1 ) ^{3}})

ln (e x y)

ln (1 + e) - ln (2)

ln ∣ x - 1 ∣ - ln ∣ x + 1 ∣

2 ln (x) + ln (2 x + 3)

What is log_{10}(x)+log_{10}(y)-2log_{10}(z) ?
The solution to log_{10}(x)+log_{10}(y)-2log_{10}(z) is log_{10}((xy)/(z^2))