What is log_{10}((sqrt(x))/(x^2)) ?

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

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simplify log_{10}((sqrt(x))/(x^2))

simplify

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

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

Solution steps

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

Cancel

\frac{x}{x ^{2}} : \frac{1}{x x}

= lo g_{10} (\frac{1}{x x})

Simplify

\frac{1}{x x} : (x x)^{- 1}

= lo g_{10} ((x x)^{- 1})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} ((x x)^{- 1}) = - 1 \cdot lo g_{10} (x x)

= - 1 \cdot lo g_{10} (x x)

Apply rule:

1 \cdot a = a

= - lo g_{10} (x x)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

Apply the distributive law:

- (a + b) = - a - b

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

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

[y (ln (x) - ln (y)) + x] d x + x (ln (y) - ln (x)) d y

6 ln (x) - 2 ln (y)

ln (\frac{x ^{3} x - 1}{3 x - 12})

2 ln (\frac{5}{4})

lo g_{2} (\frac{ab}{4})

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