What is log_{10}((z^2)/(xy^4)) ?

The solution to log_{10}((z^2)/(xy^4)) is 2log_{10}(z)-log_{10}(x)-4log_{10}(y)

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simplify log_{10}((z^2)/(xy^4))

simplify

lo g_{10} (\frac{z ^{2}}{x y ^{4}})

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

Solution steps

lo g_{10} (\frac{z ^{2}}{x y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{z ^{2}}{x y ^{4}}) = lo g_{10} (z^{2}) - lo g_{10} (x y^{4})

= lo g_{10} (z^{2}) - lo g_{10} (x y^{4})

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

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

= 2 lo g_{10} (z) - (lo g_{10} (x) + 4 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

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

= 2 lo g_{10} (z) - lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{10} (0.24 x 1 0^{6})

lo g_{2} (\frac{a ^{2} - 4}{9})

\frac{1}{3} lo g_{c} (x) + 2 lo g_{c} (y) - 4 lo g_{c} (x)

lo g_{10} (3) + lo g_{10} (6) - lo g_{10} (2)

ln (y^{3}) + \frac{1}{3} ln (x^{3} y^{6}) - 5 ln (y)

What is log_{10}((z^2)/(xy^4)) ?
The solution to log_{10}((z^2)/(xy^4)) is 2log_{10}(z)-log_{10}(x)-4log_{10}(y)