What is 3ln(x)-(ln(4x)+2ln(v)) ?

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

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simplify 3ln(x)-(ln(4x)+2ln(v))

simplify

3 ln (x) - (ln (4 x) + 2 ln (v))

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

Solution steps

3 ln (x) - (ln (4 x) + 2 ln (v))

Apply log rule:

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

2 ln (v) = ln (v^{2})

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

Apply log rule:

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

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

= 3 ln (x) - ln (4 x v^{2})

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln (x^{3}) - ln (4 x v^{2})

Apply log rule:

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

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

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

Cancel the common factor:

x

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

ln (\frac{x}{3 x + 1})

- lo g_{10} (1.9 \cdot 1 0^{- 8})

ln (6) + ln (\frac{e ^{(2.47519)}}{3})

9 ln (x) - ln ((\frac{y}{x})^{2} + 1 + \frac{y}{x})

2 lo g_{a} (x) - 3 lo g_{a} (y)

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