What is 10log_{10}(1/(1+(2pi*400*5.03*9.566)^2)) ?

The solution to 10log_{10}(1/(1+(2pi*400*5.03*9.566)^2)) is -10log_{10}(38493.584^2pi^2+1)

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simplify 10log_{10}(1/(1+(2pi4005.03*9.566)^2))

simplify

10 lo g_{10} (\frac{1}{1 + ( 2 π \cdot 400 \cdot 5.03 \cdot 9.566 ) ^{2}})

- 10 lo g_{10} (38493.58 4^{2} π^{2} + 1)

Decimal Notation

- 101.65076 \dots

Solution steps

10 lo g_{10} (\frac{1}{1 + ( 2 π 400 \cdot 5.03 \cdot 9.566 ) ^{2}})

Apply log rule:

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

lo g_{10} (\frac{1}{1 + ( 2 π 400 \cdot 5.03 \cdot 9.566 ) ^{2}}) = lo g_{10} (1) - lo g_{10} (1 + (2 π 400 \cdot 5.03 \cdot 9.566)^{2})

= 10 (lo g_{10} (1) - lo g_{10} ((2 \cdot 400 \cdot 5.03 \cdot 9.566 π)^{2} + 1))

Apply log rule:

lo g_{a} (1) = 0

= 10 (- lo g_{10} ((2 \cdot 400 \cdot 5.03 \cdot 9.566 π)^{2} + 1) + 0)

(2 π 400 \cdot 5.03 \cdot 9.566)^{2} = 38493.58 4^{2} π^{2}

= 10 (- lo g_{10} (38493.58 4^{2} π^{2} + 1) + 0)

0 - lo g_{10} (1 + 38493.58 4^{2} π^{2}) = - lo g_{10} (1 + 38493.58 4^{2} π^{2})

= 10 (- lo g_{10} (38493.58 4^{2} π^{2} + 1))

Remove parentheses:

(- a) = - a

= - 10 lo g_{10} (38493.58 4^{2} π^{2} + 1)

\frac{ln ( \frac{162}{5} )}{3 ln ( 3 )}

2 \cdot ln (\frac{1}{6})

\frac{( ln ( 20 ) + ln ( 25 ) )}{3 ln ( 5 )}

\frac{1}{2} ln (9 x^{2}) + 2 ln (x) - 3 ln (2 x)

- 2 ln ∣ ln (x) ∣ - ln (x)

What is 10log_{10}(1/(1+(2pi*400*5.03*9.566)^2)) ?
The solution to 10log_{10}(1/(1+(2pi*400*5.03*9.566)^2)) is -10log_{10}(38493.584^2pi^2+1)