What is 2ln(x/(3-x))-ln(4) ?

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

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simplify 2ln(x/(3-x))-ln(4)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( \frac{x}{3 - x} ) ^{2}}{4} : \frac{x ^{2}}{4 ( 3 - x ) ^{2}}

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

lo g_{10} (4) + 3 lo g_{10} (1.025)

ln (\frac{6.5}{17})

ln (760) - ln (5.9)

ln (e^{- x} + 1) - ln (e^{x} + 1)

lo g_{e} (10 e)

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