What is log_{10}((sqrt(x))/(1000y^3)) ?

The solution to log_{10}((sqrt(x))/(1000y^3)) is log_{10}(sqrt(x))-3-3log_{10}(y)

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simplify log_{10}((sqrt(x))/(1000y^3))

simplify

lo g_{10} (\frac{x}{1000 y ^{3}})

lo g_{10} (x) - 3 - 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{1000 y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x}{1000 y ^{3}}) = lo g_{10} (x) - lo g_{10} (1000 y^{3})

= lo g_{10} (x) - lo g_{10} (1000 y^{3})

Simplify

lo g_{10} (1000 y^{3}) : 3 + 3 lo g_{10} (y)

= lo g_{10} (x) - (3 + 3 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (3 + 3 lo g_{10} (y)) = - 3 - 3 lo g_{10} (y)

= lo g_{10} (x) - 3 - 3 lo g_{10} (y)

\frac{1}{2} (- 5 lo g_{10} (x) + lo g_{10} (y z^{3}))

\frac{ln ( \frac{1034}{40353607} )}{2 ln ( 7 )}

lo g_{a} (5 x)

ln (\frac{5 x - 1}{x + 1})

lo g_{10} (\frac{a ^{2}}{x})

What is log_{10}((sqrt(x))/(1000y^3)) ?
The solution to log_{10}((sqrt(x))/(1000y^3)) is log_{10}(sqrt(x))-3-3log_{10}(y)