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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (y^{5} x) : 5 lo g_{10} (y) + lo g_{10} (x)

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

2 lo g_{10} (x) - 4 lo g_{10} (x + 5) + \frac{1}{x} lo g_{10} (3 x + 5)

ln (\frac{4}{7 x ^{7} y})

- \frac{5}{8} lo g_{2} (\frac{5}{8}) - \frac{3}{8} lo g_{2} (\frac{3}{8})

ln (\frac{e ^{5}}{6})

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