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

The solution to 1/2 ln(4)-2ln(x) is ln(2/(x^2))

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simplify 1/2 ln(4)-2ln(x)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

4^{\frac{1}{2}} = 2

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

ln ((\frac{y - 1}{3})^{2})

3 ln (x) + ln (x^{4}) - ln (x^{3} e^{x})

lo g_{4} (16 x^{4} y^{3})

ln (\frac{L ^{5} M ^{2}}{K})

ln (\frac{( x + 2 ) ^{4} y ^{\frac{1}{3}}}{( w - 1 ) ^{3}})