What is ln(x)-1/4 ln(v^2+2) ?

The solution to ln(x)-1/4 ln(v^2+2) is ln((x(v^2+2)^{3/4})/(v^2+2))

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simplify ln(x)-1/4 ln(v^2+2)

simplify

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

ln \frac{x ( v ^{2} + 2 ) ^{\frac{3}{4}}}{v ^{2} + 2}

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{4} ln (v^{2} + 2) = ln ((v^{2} + 2)^{\frac{1}{4}})

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

Apply log rule:

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

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

= ln (\frac{x}{( v ^{2} + 2 ) ^{\frac{1}{4}}})

Simplify

\frac{x}{( v ^{2} + 2 ) ^{\frac{1}{4}}} : \frac{x ( v ^{2} + 2 ) ^{\frac{3}{4}}}{v ^{2} + 2}

= ln \frac{x ( v ^{2} + 2 ) ^{\frac{3}{4}}}{v ^{2} + 2}

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What is ln(x)-1/4 ln(v^2+2) ?
The solution to ln(x)-1/4 ln(v^2+2) is ln((x(v^2+2)^{3/4})/(v^2+2))