What is 20log_{10}(P/(2*10^{-4)}) ?

The solution to 20log_{10}(P/(2*10^{-4)}) is 20(log_{10}(P)+log_{10}(5000))

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simplify 20log_{10}(P/(2*10^{-4)})

simplify

20 lo g_{10} (\frac{P}{2 \cdot 1 0 ^{- 4}})

20 (lo g_{10} (P) + lo g_{10} (5000))

Solution steps

20 lo g_{10} (\frac{P}{2 \cdot 1 0 ^{- 4}})

Apply log rule:

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

lo g_{10} (\frac{P}{2 \cdot 1 0 ^{- 4}}) = lo g_{10} (P) - lo g_{10} (2 \cdot 1 0^{- 4})

= 20 (lo g_{10} (P) - lo g_{10} (1 0^{- 4} \cdot 2))

Multiply

2 \cdot 1 0^{- 4} : \frac{1}{5000}

= 20 (lo g_{10} (P) - lo g_{10} (\frac{1}{5000}))

Apply log rule:

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

= 20 (lo g_{10} (P) - (- lo g_{10} (5000)))

Apply rule

- (- a) = a

= 20 (lo g_{10} (P) + lo g_{10} (5000))

\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x - 2 ∣

- ln (3) + ln (2) + ln (2) - ln (1)

ln (p) + ln (1 - p)

- lo g_{10} (7.8 \cdot 1 0^{- 3})

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

What is 20log_{10}(P/(2*10^{-4)}) ?
The solution to 20log_{10}(P/(2*10^{-4)}) is 20(log_{10}(P)+log_{10}(5000))