What is log_{10}((sqrt(x))/(100y^8)) ?

The solution to log_{10}((sqrt(x))/(100y^8)) is log_{10}(sqrt(x))-2-8log_{10}(y)

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simplify log_{10}((sqrt(x))/(100y^8))

simplify

lo g_{10} (\frac{x}{100 y ^{8}})

lo g_{10} (x) - 2 - 8 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{100 y ^{8}})

Apply log rule:

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

lo g_{10} (\frac{x}{100 y ^{8}}) = lo g_{10} (x) - lo g_{10} (100 y^{8})

= lo g_{10} (x) - lo g_{10} (100 y^{8})

Simplify

lo g_{10} (100 y^{8}) : 2 + 8 lo g_{10} (y)

= lo g_{10} (x) - (2 + 8 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 + 8 lo g_{10} (y)) = - 2 - 8 lo g_{10} (y)

= lo g_{10} (x) - 2 - 8 lo g_{10} (y)

lo g_{b} (x yz)

3 ln (x) + 6 ln (y) - 4 ln (z)

4 ln (x) - \frac{1}{4} ln (y)

lo g_{2} (\frac{8}{x + 7})

lo g_{2} (2 x + 1) - 5 lo g_{4} (x^{2}) + 4 lo g_{2} (x)

What is log_{10}((sqrt(x))/(100y^8)) ?
The solution to log_{10}((sqrt(x))/(100y^8)) is log_{10}(sqrt(x))-2-8log_{10}(y)