What is log_{10}(z/(sqrt(y^3)x^2)) ?

The solution to log_{10}(z/(sqrt(y^3)x^2)) is log_{10}(z)-log_{10}(y)-log_{10}(sqrt(y))-2log_{10}(x)

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simplify log_{10}(z/(sqrt(y^3)x^2))

simplify

lo g_{10} (\frac{z}{y ^{3} x ^{2}})

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

Solution steps

lo g_{10} (\frac{z}{y ^{3} x ^{2}})

Simplify

y^{3} : y y

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

lo g_{10} (y y x^{2}) : lo g_{10} (y) + lo g_{10} (y) + 2 lo g_{10} (x)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

ln (2 x^{2}) + ln (5 x^{7})

lo g_{10} (y x^{3})

lo g_{10} (x) - lo g_{10} (x + 1)

lo g_{2} (x^{2}) - 3 lo g_{2} (x) - 28

2 (ln ∣ a + 2 ∣ - ln ∣ a ∣)

What is log_{10}(z/(sqrt(y^3)x^2)) ?
The solution to log_{10}(z/(sqrt(y^3)x^2)) is log_{10}(z)-log_{10}(y)-log_{10}(sqrt(y))-2log_{10}(x)