What is 20*log_{10}((10)/(10*n)) ?

The solution to 20*log_{10}((10)/(10*n)) is -20log_{10}(n)

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simplify 20log_{10}((10)/(10n))

simplify

20 \cdot lo g_{10} (\frac{10}{10 \cdot n})

- 20 lo g_{10} (n)

Solution steps

20 lo g_{10} (\frac{10}{10 n})

Simplify

\frac{10}{10 n} : \frac{1}{n}

= 20 lo g_{10} (\frac{1}{n})

Simplify

\frac{1}{n} : n^{- 1}

= 20 lo g_{10} (n^{- 1})

Apply log rule

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

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

= 20 (- 1 \cdot lo g_{10} (n))

Apply rule:

1 \cdot a = a

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

= 20 (- lo g_{10} (n))

Apply rule:

a (- b) = - ab

20 (- lo g_{10} (n)) = - 20 lo g_{10} (n)

= - 20 lo g_{10} (n)

(x + y) (x^{2} + 2 x y + y^{2})

\frac{x + 4 + \frac{3}{x}}{x - 4 - \frac{5}{x}}

sin^{3} (x) + sin (x) cos^{2} (x)

(r cos (x))^{2}

- 4 x + 3 x

What is 20*log_{10}((10)/(10*n)) ?
The solution to 20*log_{10}((10)/(10*n)) is -20log_{10}(n)