What is simplify-ln(V/(Nx))-ln((bV)/(Nx)) ?

The solution to simplify-ln(V/(Nx))-ln((bV)/(Nx)) is -ln((bV^2)/(N^2x^2))

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simplify-ln(V/(Nx))-ln((bV)/(Nx))

simplify

- ln (\frac{V}{N x}) - ln (\frac{bV}{N x})

- ln (\frac{b V ^{2}}{N ^{2} x ^{2}})

Solution steps

- ln (\frac{V}{N x}) - ln (\frac{bV}{N x})

Rewrite

- ln (\frac{V}{N x}) - ln (\frac{bV}{N x})

- (ln (\frac{V}{N x}) + ln (\frac{bV}{N x}))

= - (ln (\frac{V}{N x}) + ln (\frac{bV}{N x}))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{V}{N x}) + ln (\frac{bV}{N x}) = ln (\frac{V}{N x} \cdot \frac{bV}{N x})

= - ln (\frac{V}{N x} \cdot \frac{bV}{N x})

Simplify

\frac{V}{N x} \cdot \frac{bV}{N x} : \frac{b V ^{2}}{N ^{2} x ^{2}}

= - ln (\frac{b V ^{2}}{N ^{2} x ^{2}})

ln (2 v^{2} + 1) - 2 ln (v^{2} + 1) - 2 ln (y)

ln (80) + ln (20)

ln (y) + ln (\frac{x}{y} + 1)

ln ∣ x ∣ + ln ∣ x - 1 ∣ + ln ∣ x + 1 ∣

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

What is simplify-ln(V/(Nx))-ln((bV)/(Nx)) ?
The solution to simplify-ln(V/(Nx))-ln((bV)/(Nx)) is -ln((bV^2)/(N^2x^2))