What is 20log_{10}((4.2)/(2sqrt(2))) ?

The solution to 20log_{10}((4.2)/(2sqrt(2))) is 20(log_{10}(4.2)-3/2 log_{10}(2))

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simplify 20log_{10}((4.2)/(2sqrt(2)))

simplify

20 lo g_{10} (\frac{4.2}{2 2})

20 (lo g_{10} (4.2) - \frac{3}{2} lo g_{10} (2))

Decimal Notation

3.43408 \dots

Solution steps

20 lo g_{10} (\frac{4.2}{2 2})

Apply log rule:

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

lo g_{10} (\frac{4.2}{2 2}) = lo g_{10} (4.2) - lo g_{10} (22)

= 20 (lo g_{10} (4.2) - lo g_{10} (22))

lo g_{10} (22) = \frac{3}{2} lo g_{10} (2)

= 20 (lo g_{10} (4.2) - \frac{3}{2} lo g_{10} (2))

f (x) = ln (5) + ln (7) - 3 ln^{2} (x)

2 (1 - 2 ln (1) + 3 - 2 ln (3) + 5 - 2 ln (5) + 7 - 2 ln (7))

\frac{1}{2} ln (50) + \frac{1}{2} ln (1 - \frac{1}{2})

ln (\frac{n + 2}{n + 1})

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

What is 20log_{10}((4.2)/(2sqrt(2))) ?
The solution to 20log_{10}((4.2)/(2sqrt(2))) is 20(log_{10}(4.2)-3/2 log_{10}(2))