What is 10log_{10}(((2.5*10^{-3}))/(1000))+40+59 ?

The solution to 10log_{10}(((2.5*10^{-3}))/(1000))+40+59 is 10log_{10}((2.5)/(1000))+69

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simplify 10log_{10}(((2.5*10^{-3}))/(1000))+40+59

simplify

10 lo g_{10} (\frac{( 2.5 \cdot 1 0 ^{- 3} )}{1000}) + 40 + 59

10 lo g_{10} (\frac{2.5}{1000}) + 69

Decimal Notation

42.97940 \dots

Solution steps

10 lo g_{10} (\frac{( 2.5 \cdot 1 0 ^{- 3} )}{1000}) + 40 + 59

Apply log rule:

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

lo g_{10} (\frac{( 2.5 \cdot 1 0 ^{- 3} )}{1000}) = lo g_{10} ((2.5 \cdot 1 0^{- 3})) - lo g_{10} (1000)

= 10 (lo g_{10} (1 0^{- 3} \cdot 2.5) - lo g_{10} (1000)) + 40 + 59

10 (lo g_{10} (2.5 \cdot 1 0^{- 3}) - lo g_{10} (1000)) = 10 (lo g_{10} (\frac{2.5}{1000}) - 3)

= 10 (lo g_{10} (\frac{2.5}{1000}) - 3) + 40 + 59

Expand

10 (lo g_{10} (\frac{2.5}{1000}) - 3) : 10 lo g_{10} (\frac{2.5}{1000}) - 30

= 10 lo g_{10} (\frac{2.5}{1000}) - 30 + 40 + 59

Add/Subtract the numbers:

- 30 + 40 + 59 = 69

= 10 lo g_{10} (\frac{2.5}{1000}) + 69

ln (\frac{\frac{2}{3} x + 1}{\frac{2}{3} x - 1})

ln (10000) - ln (5000) + 5

ln (\frac{24}{5})

+ \frac{ln ( 1.5575 )}{ln ( \frac{2}{25} ) - ln ( 0.239 )}

ln (4^{\frac{1}{2}}) - ln (x^{2})

What is 10log_{10}(((2.5*10^{-3}))/(1000))+40+59 ?
The solution to 10log_{10}(((2.5*10^{-3}))/(1000))+40+59 is 10log_{10}((2.5)/(1000))+69