What is simplify-20log_{10}((0.125)/(4pi*5000)) ?

The solution to simplify-20log_{10}((0.125)/(4pi*5000)) is -20(log_{10}(0.125)-log_{10}(20000pi))

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simplify-20log_{10}((0.125)/(4pi*5000))

simplify

- 20 lo g_{10} (\frac{0.125}{4 π \cdot 5000})

- 20 (lo g_{10} (0.125) - lo g_{10} (20000 π))

Decimal Notation

114.02539 \dots

Solution steps

- 20 lo g_{10} (\frac{0.125}{4 π 5000})

Apply log rule:

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

lo g_{10} (\frac{0.125}{4 π 5000}) = lo g_{10} (0.125) - lo g_{10} (4 π 5000)

= - 20 (lo g_{10} (0.125) - lo g_{10} (4 \cdot 5000 π))

Multiply the numbers:

4 \cdot 5000 = 20000

= - 20 (lo g_{10} (0.125) - lo g_{10} (20000 π))

ln (\frac{1000}{1042})

ln (v) - ln (x)

- \frac{ln ( 5 ) - ln ( 4 )}{10}

ln (\frac{73}{117})

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

What is simplify-20log_{10}((0.125)/(4pi*5000)) ?
The solution to simplify-20log_{10}((0.125)/(4pi*5000)) is -20(log_{10}(0.125)-log_{10}(20000pi))