What is log_{10}((sqrt(x))/(100y^4)) ?

The solution to log_{10}((sqrt(x))/(100y^4)) is log_{10}(sqrt(x))-2-4log_{10}(y)

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simplify log_{10}((sqrt(x))/(100y^4))

simplify

lo g_{10} (\frac{x}{100 y ^{4}})

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

Solution steps

lo g_{10} (\frac{x}{100 y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x}{100 y ^{4}}) = lo g_{10} (x) - lo g_{10} (100 y^{4})

= lo g_{10} (x) - lo g_{10} (100 y^{4})

Simplify

lo g_{10} (100 y^{4}) : 2 + 4 lo g_{10} (y)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

5 lo g_{b} (q) + 2 lo g_{b} (y)

- 0.35 lo g_{2} (0.35) - 0.65 lo g_{2} (0.65)

5 lo g_{b} (q) - lo g_{b} (r)

lo g_{2} (a) + lo g_{2} (b)

lo g_{10} (x (x + 1)^{4})

What is log_{10}((sqrt(x))/(100y^4)) ?
The solution to log_{10}((sqrt(x))/(100y^4)) is log_{10}(sqrt(x))-2-4log_{10}(y)