What is log_{10}((sqrt(x))/(100y^6)) ?

The solution to log_{10}((sqrt(x))/(100y^6)) is log_{10}(sqrt(x))-2-6log_{10}(y)

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simplify log_{10}((sqrt(x))/(100y^6))

simplify

lo g_{10} (\frac{x}{100 y ^{6}})

lo g_{10} (x) - 2 - 6 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{100 y ^{6}})

Apply log rule:

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

lo g_{10} (\frac{x}{100 y ^{6}}) = lo g_{10} (x) - lo g_{10} (100 y^{6})

= lo g_{10} (x) - lo g_{10} (100 y^{6})

Simplify

lo g_{10} (100 y^{6}) : 2 + 6 lo g_{10} (y)

= lo g_{10} (x) - (2 + 6 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 + 6 lo g_{10} (y)) = - 2 - 6 lo g_{10} (y)

= lo g_{10} (x) - 2 - 6 lo g_{10} (y)

lo g_{10} (x^{\frac{1}{2}}) + lo g_{10} ((x + 1)^{3})

lo g_{2} (12) + lo g_{2} (3) - 2 lo g_{2} (2)

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

lo g_{5} (25 z)

- \frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1) + C

What is log_{10}((sqrt(x))/(100y^6)) ?
The solution to log_{10}((sqrt(x))/(100y^6)) is log_{10}(sqrt(x))-2-6log_{10}(y)