What is 1/2 [ln(3)+4ln(x)-2ln(x-1)] ?

The solution to 1/2 [ln(3)+4ln(x)-2ln(x-1)] is 1/2 ln((3x^4)/((x-1)^2))

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simplify 1/2 [ln(3)+4ln(x)-2ln(x-1)]

simplify

\frac{1}{2} [ln (3) + 4 ln (x) - 2 ln (x - 1)]

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

Solution steps

\frac{1}{2} [ln (3) + 4 ln (x) - 2 ln (x - 1)]

Apply log rule:

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

4 ln (x) = ln (x^{4})

= \frac{1}{2} [ln (x^{4}) - 2 ln (x - 1) + ln (3)]

Apply log rule:

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

ln (3) + ln (x^{4}) = ln (3 x^{4})

= \frac{1}{2} [ln (3 x^{4}) - 2 ln (x - 1)]

Apply log rule:

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

2 ln (x - 1) = ln ((x - 1)^{2})

= \frac{1}{2} [ln (3 x^{4}) - ln ((x - 1)^{2})]

Apply log rule:

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

ln (3 x^{4}) - ln ((x - 1)^{2}) = ln (\frac{3 x ^{4}}{( x - 1 ) ^{2}})

= \frac{1}{2} [ln (\frac{3 x ^{4}}{( x - 1 ) ^{2}})]

Remove parentheses:

(a) = a

= \frac{1}{2} ln (\frac{3 x ^{4}}{( x - 1 ) ^{2}})

\frac{( 0.5 ln ( 28 ) - ln ( 2 ) )}{0.5}

\frac{1}{2} ln (\frac{11}{3})

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

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

\frac{1}{2} ln (17.6 + 1) + 2 ln (8.8 - 1) + C

What is 1/2 [ln(3)+4ln(x)-2ln(x-1)] ?
The solution to 1/2 [ln(3)+4ln(x)-2ln(x-1)] is 1/2 ln((3x^4)/((x-1)^2))