What is 10*log_{10}(0.1*((0.125)/(4*pi*8))^2) ?

The solution to 10*log_{10}(0.1*((0.125)/(4*pi*8))^2) is 10log_{10}(0.1)+20log_{10}((0.125)/(32pi))

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simplify 10log_{10}(0.1((0.125)/(4pi8))^2)

simplify

10 \cdot lo g_{10} (0.1 \cdot (\frac{0.125}{4 \cdot π \cdot 8})^{2})

10 lo g_{10} (0.1) + 20 lo g_{10} (\frac{0.125}{32 π})

Decimal Notation

- 68.10779 \dots

Solution steps

10 lo g_{10} (0.1 (\frac{0.125}{4 π 8})^{2})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

10 lo g_{10} (0.1 (\frac{0.125}{4 π 8})^{2}) = 10 lo g_{10} (0.1) + 10 lo g_{10} ((\frac{0.125}{4 π 8})^{2})

= 10 lo g_{10} (0.1) + 10 lo g_{10} ((\frac{0.125}{4 \cdot 8 π})^{2})

Apply log rule:

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

lo g_{10} ((\frac{0.125}{4 π 8})^{2}) = 2 lo g_{10} (\frac{0.125}{4 π 8})

= 10 lo g_{10} (0.1) + 10 \cdot 2 lo g_{10} (\frac{0.125}{4 π 8})

10 \cdot 2 lo g_{10} (\frac{0.125}{4 π 8}) = 20 lo g_{10} (\frac{0.125}{32 π})

= 10 lo g_{10} (0.1) + 20 lo g_{10} (\frac{0.125}{32 π})

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

ln (\frac{n !}{x ^{n + 1}})

ln (\frac{x ^{2}}{sin ^{3} ( x )})

- 0.1 ln (0.1) - (1 - 0.1) ln (1 - 0.1)

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

What is 10*log_{10}(0.1*((0.125)/(4*pi*8))^2) ?
The solution to 10*log_{10}(0.1*((0.125)/(4*pi*8))^2) is 10log_{10}(0.1)+20log_{10}((0.125)/(32pi))