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

The solution to 3ln(2)+2ln(x)-1/2 ln(x-4) is ln((8x^2sqrt(x-4))/(x-4))

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

simplify

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

ln (\frac{8 x ^{2} x - 4}{x - 4})

Solution steps

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

Apply log rule:

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

3 ln (2) = ln (2^{3})

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (2^{3}) + ln (x^{2}) = ln (2^{3} x^{2})

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

2^{3} = 8

= ln (8 x^{2}) - \frac{1}{2} ln (x - 4)

Apply log rule:

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

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

= ln (8 x^{2}) - ln ((x - 4)^{\frac{1}{2}})

Apply log rule:

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

ln (8 x^{2}) - ln ((x - 4)^{\frac{1}{2}}) = ln (\frac{8 x ^{2}}{( x - 4 ) ^{\frac{1}{2}}})

= ln (\frac{8 x ^{2}}{( x - 4 ) ^{\frac{1}{2}}})

Simplify

\frac{8 x ^{2}}{( x - 4 ) ^{\frac{1}{2}}} : \frac{8 x ^{2} x - 4}{x - 4}

= ln (\frac{8 x ^{2} x - 4}{x - 4})

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

2 ln (x) + ln (y) - 4 x - y

\frac{4}{3} ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ x - 4 ∣

\frac{1}{2} lo g_{b} (3) + 3 lo g_{b} (13) - 3 lo g_{b} (2)

ln (u - 2) - ln (u + 2)

What is 3ln(2)+2ln(x)-1/2 ln(x-4) ?
The solution to 3ln(2)+2ln(x)-1/2 ln(x-4) is ln((8x^2sqrt(x-4))/(x-4))