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))

2000 ln (\frac{14000}{14000 - 2100 ( 1 )}) - 9.8 (1)

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

ln (\frac{tan ^{2} ( x )}{e ^{4 x^{2}} ∣ x ^{5} ∣})

ln (e^{- 9 θ} \frac{θ ^{9}}{9 !})

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

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))