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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{10} (18) - lo g_{10} (6)

lo g_{3} (2) + lo g_{3} (13)

2 lo g_{5} (x) - lo g_{5} (y) - \frac{1}{2} lo g_{5} (z)

lo g_{10} (\frac{1000 c ^{5}}{2 d ^{4}})

lo g_{2} (2000) - lo g_{2} (150)

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