What is log_{10}((x^5)/(sqrt(z)y)) ?

The solution to log_{10}((x^5)/(sqrt(z)y)) is 5log_{10}(x)-log_{10}(sqrt(z))-log_{10}(y)

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simplify log_{10}((x^5)/(sqrt(z)y))

simplify

lo g_{10} (\frac{x ^{5}}{z y})

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

Solution steps

lo g_{10} (\frac{x ^{5}}{z y})

Apply log rule:

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

lo g_{10} (\frac{x ^{5}}{z y}) = lo g_{10} (x^{5}) - lo g_{10} (z y)

= lo g_{10} (x^{5}) - lo g_{10} (z y)

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

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

= 5 lo g_{10} (x) - (lo g_{10} (z) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

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

= 5 lo g_{10} (x) - lo g_{10} (z) - lo g_{10} (y)

ln (x) - ln (12)

ln (x) - ln (17)

lo g_{5} (\frac{125}{x + 4})

lo g_{10} (m) + lo g_{10} (n) - lo g_{10} (p)

lo g_{4} (\frac{64}{y})

What is log_{10}((x^5)/(sqrt(z)y)) ?
The solution to log_{10}((x^5)/(sqrt(z)y)) is 5log_{10}(x)-log_{10}(sqrt(z))-log_{10}(y)