What is 10log_{10}((2/pi)/(10^{-12)}) ?

The solution to 10log_{10}((2/pi)/(10^{-12)}) is 10(log_{10}(2/pi)--12log_{10}(10))

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simplify 10log_{10}((2/pi)/(10^{-12)})

simplify

10 lo g_{10} (\frac{\frac{2}{π}}{1 0 ^{- 12}})

10 (lo g_{10} (\frac{2}{π}) - - 12 lo g_{10} (10))

Decimal Notation

- 121.96119 \dots

Solution steps

10 lo g_{10} (\frac{\frac{2}{π}}{1 0 ^{- 12}})

Apply log rule:

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

lo g_{10} (\frac{\frac{2}{π}}{1 0 ^{- 12}}) = lo g_{10} (\frac{2}{π}) - lo g_{10} (1 0^{- 12})

= 10 (lo g_{10} (\frac{2}{π}) - lo g_{10} (1 0^{- 12}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 12}) = - 12 lo g_{10} (10)

= 10 (lo g_{10} (\frac{2}{π}) - - 12 lo g_{10} (10))

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

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

lo g_{2} (a + b) + lo g_{2} (a - b) - 2 lo g_{2} (a)

36 \cdot ln (9) - 36 \cdot ln (4)

What is 10log_{10}((2/pi)/(10^{-12)}) ?
The solution to 10log_{10}((2/pi)/(10^{-12)}) is 10(log_{10}(2/pi)--12log_{10}(10))