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

The solution to log_{10}((sqrt(x))/(10y^8)) is log_{10}(sqrt(x))-1-8log_{10}(y)

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

simplify

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

lo g_{10} (x) - 1 - 8 lo g_{10} (y)

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (10 y^{8}) : 1 + 8 lo g_{10} (y)

= lo g_{10} (x) - (1 + 8 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (1 + 8 lo g_{10} (y)) = - 1 - 8 lo g_{10} (y)

= lo g_{10} (x) - 1 - 8 lo g_{10} (y)

lo g_{b} (\frac{x}{( yz ) ^{2}})

2 lo g_{10} (x) - 7 lo g_{10} (y)

ln (x^{5}) - ln (x)

\frac{1}{2} lo g_{b} (57) + \frac{1}{2} lo g_{b} (74)

ln (2 e^{2 x})

What is log_{10}((sqrt(x))/(10y^8)) ?
The solution to log_{10}((sqrt(x))/(10y^8)) is log_{10}(sqrt(x))-1-8log_{10}(y)