What is ln|b|ln(b/a)+(-ln(|b|^2)+ln(|a|^2))/2 ?

The solution to ln|b|ln(b/a)+(-ln(|b|^2)+ln(|a|^2))/2 is ln|b|ln(b/a)+(ln((a^2)/(b^2)))/2

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simplify ln|b|ln(b/a)+(-ln(|b|^2)+ln(|a|^2))/2

simplify

ln ∣ b ∣ ln (\frac{b}{a}) + \frac{- ln ( ∣ b ∣ ^{2} ) + ln ( ∣ a ∣ ^{2} )}{2}

ln ∣ b ∣ ln (\frac{b}{a}) + \frac{ln ( \frac{a ^{2}}{b ^{2}} )}{2}

Solution steps

ln ∣ b ∣ ln (\frac{b}{a}) + \frac{- ln ( ∣ b ∣ ^{2} ) + ln ( ∣ a ∣ ^{2} )}{2}

Apply log rule:

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

ln (∣ a ∣^{2}) - ln (∣ b ∣^{2}) = ln (\frac{∣ a ∣ ^{2}}{∣ b ∣ ^{2}})

= ln ∣ b ∣ ln (\frac{b}{a}) + \frac{ln ( \frac{∣ a ∣ ^{2}}{∣ b ∣ ^{2}} )}{2}

Simplify

\frac{∣ a ∣ ^{2}}{∣ b ∣ ^{2}} : \frac{a ^{2}}{b ^{2}}

= ln ∣ b ∣ ln (\frac{b}{a}) + \frac{ln ( \frac{a ^{2}}{b ^{2}} )}{2}

0 \cdot lo g_{10} (0.69) + (1 - 0) \cdot lo g_{10} (1 - 0.69)

lo g_{5} (\frac{1}{20})

- lo g_{10} (3.2 \cdot 1 0^{- 6})

\frac{1}{0.00499} ln (\frac{400 - 15}{75 - 15})

10 lo g_{10} (\frac{1 0 ^{- 6} + 1 0 ^{- 6}}{1 0 ^{- 12}})

What is ln|b|ln(b/a)+(-ln(|b|^2)+ln(|a|^2))/2 ?
The solution to ln|b|ln(b/a)+(-ln(|b|^2)+ln(|a|^2))/2 is ln|b|ln(b/a)+(ln((a^2)/(b^2)))/2