What is 10*log_{10}((5*10^{-3})/1) ?

The solution to 10*log_{10}((5*10^{-3})/1) is -10log_{10}(200)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 10log_{10}((510^{-3})/1)

simplify

10 \cdot lo g_{10} (\frac{5 \cdot 1 0 ^{- 3}}{1})

- 10 lo g_{10} (200)

Decimal Notation

- 23.01029 \dots

Solution steps

10 lo g_{10} (\frac{5 \cdot 1 0 ^{- 3}}{1})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{5 \cdot 1 0 ^{- 3}}{1}) = lo g_{10} (5 \cdot 1 0^{- 3}) - lo g_{10} (1)

= 10 (lo g_{10} (1 0^{- 3} \cdot 5) - lo g_{10} (1))

Multiply

5 \cdot 1 0^{- 3} : \frac{1}{200}

= 10 (lo g_{10} (\frac{1}{200}) - lo g_{10} (1))

Apply log rule:

lo g_{a} (1) = 0

= 10 (lo g_{10} (\frac{1}{200}) - 0)

lo g_{10} (\frac{1}{200}) - 0 = lo g_{10} (\frac{1}{200})

= 10 lo g_{10} (\frac{1}{200})

Simplify

lo g_{10} (\frac{1}{200}) : - lo g_{10} (200)

= 10 (- lo g_{10} (200))

Remove parentheses:

(- a) = - a

= - 10 lo g_{10} (200)

3 lo g_{6} (x) - \frac{1}{5} lo g_{6} (y) + 2 lo g_{6} (w)

- 100 ln (5) + 100 ln (6)

ln (\frac{2.43 x + a}{x})

\frac{1}{4} ln (10) + ln (5) - \frac{1}{2} ln (7)

ln (\frac{a ^{- 2}}{b ^{1} c ^{- 3}})

What is 10*log_{10}((5*10^{-3})/1) ?
The solution to 10*log_{10}((5*10^{-3})/1) is -10log_{10}(200)