What is log_{10}(1/(sqrt(2pik^2))) ?

The solution to log_{10}(1/(sqrt(2pik^2))) is -log_{10}(sqrt(2)sqrt(pi)sqrt(k^2))

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simplify log_{10}(1/(sqrt(2pik^2)))

simplify

lo g_{10} (\frac{1}{2 π k ^{2}})

- lo g_{10} (2 π k^{2})

Solution steps

lo g_{10} (\frac{1}{2 π k ^{2}})

Apply log rule:

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

lo g_{10} (\frac{1}{2 π k ^{2}}) = lo g_{10} (1) - lo g_{10} (2 π k^{2})

= lo g_{10} (1) - lo g_{10} (2 π k^{2})

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{10} (2 π k^{2})

2 π k^{2} = 2 π k^{2}

= 0 - lo g_{10} (2 π k^{2})

0 - lo g_{10} (2 k^{2} π) = - lo g_{10} (2 k^{2} π)

= - lo g_{10} (2 π k^{2})

\frac{ln ( 0.5 ) - ln ( 0.15 )}{ln ( 2 )}

ln (125 e^{x})

\frac{ln ( 0.17 ) + ln ( 0.19 )}{2}

- lo g_{10} (1.90691 \cdot 1 0^{- 6})

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

What is log_{10}(1/(sqrt(2pik^2))) ?
The solution to log_{10}(1/(sqrt(2pik^2))) is -log_{10}(sqrt(2)sqrt(pi)sqrt(k^2))