What is 10log_{10}(((158*10^{-9}))/(20*10^{-3)}) ?

The solution to 10log_{10}(((158*10^{-9}))/(20*10^{-3)}) is 10(log_{10}(79/500000000)+log_{10}(50))

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simplify 10log_{10}(((15810^{-9}))/(2010^{-3)})

simplify

10 lo g_{10} (\frac{( 158 \cdot 1 0 ^{- 9} )}{20 \cdot 1 0 ^{- 3}})

10 (lo g_{10} (\frac{79}{500000000}) + lo g_{10} (50))

Decimal Notation

- 51.02372 \dots

Solution steps

10 lo g_{10} (\frac{( 158 \cdot 1 0 ^{- 9} )}{20 \cdot 1 0 ^{- 3}})

Apply log rule:

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

lo g_{10} (\frac{( 158 \cdot 1 0 ^{- 9} )}{20 \cdot 1 0 ^{- 3}}) = lo g_{10} ((158 \cdot 1 0^{- 9})) - lo g_{10} (20 \cdot 1 0^{- 3})

= 10 (lo g_{10} (1 0^{- 9} \cdot 158) - lo g_{10} (1 0^{- 3} \cdot 20))

Multiply

158 \cdot 1 0^{- 9} : \frac{79}{500000000}

= 10 (lo g_{10} (\frac{79}{500000000}) - lo g_{10} (1 0^{- 3} \cdot 20))

Multiply

20 \cdot 1 0^{- 3} : \frac{1}{50}

= 10 (lo g_{10} (\frac{79}{500000000}) - lo g_{10} (\frac{1}{50}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= 10 (lo g_{10} (\frac{79}{500000000}) - (- lo g_{10} (50)))

Apply rule

- (- a) = a

= 10 (lo g_{10} (\frac{79}{500000000}) + lo g_{10} (50))

lo g_{10} (3 - x) + lo g_{10} (4 - x^{2})

ln (13) - ln (7)

\frac{1}{2} lo g_{3} (x) + \frac{2}{3} lo g_{3} (y)

3 ln (x y)

What is 10log_{10}(((158*10^{-9}))/(20*10^{-3)}) ?
The solution to 10log_{10}(((158*10^{-9}))/(20*10^{-3)}) is 10(log_{10}(79/500000000)+log_{10}(50))