What is log_{10}((sqrt(x))/(y^9z^5)) ?

The solution to log_{10}((sqrt(x))/(y^9z^5)) is log_{10}(sqrt(x))-9log_{10}(y)-5log_{10}(z)

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simplify log_{10}((sqrt(x))/(y^9z^5))

simplify

lo g_{10} (\frac{x}{y ^{9} z ^{5}})

lo g_{10} (x) - 9 lo g_{10} (y) - 5 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x}{y ^{9} z ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{9} z ^{5}}) = lo g_{10} (x) - lo g_{10} (y^{9} z^{5})

= lo g_{10} (x) - lo g_{10} (y^{9} z^{5})

Simplify

lo g_{10} (y^{9} z^{5}) : 9 lo g_{10} (y) + 5 lo g_{10} (z)

= lo g_{10} (x) - (9 lo g_{10} (y) + 5 lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (9 lo g_{10} (y) + 5 lo g_{10} (z)) = - 9 lo g_{10} (y) - 5 lo g_{10} (z)

= lo g_{10} (x) - 9 lo g_{10} (y) - 5 lo g_{10} (z)

lo g_{4} (11) - lo g_{4} (9)

4 ln (3 x) - ln (9 x)

lo g_{10} (z \cdot w x \cdot y)

4 lo g_{5} (x) - lo g_{5} (125)

ln (\frac{x ^{2} - 2}{x ^{2} + 4})

What is log_{10}((sqrt(x))/(y^9z^5)) ?
The solution to log_{10}((sqrt(x))/(y^9z^5)) is log_{10}(sqrt(x))-9log_{10}(y)-5log_{10}(z)