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

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

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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)

\frac{3}{8} \cdot ln (\frac{8}{3}) + \frac{10}{16} \cdot ln (\frac{16}{5})

lo g_{9} (\frac{4 x}{y ^{5}})

ln (2 (e^{e}))

3 lo g_{10} (a) + lo g_{10} (b) - \frac{1}{2} lo g_{10} (c)

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