What is 4ln(2)+2ln(x)-12ln(x+3) ?

The solution to 4ln(2)+2ln(x)-12ln(x+3) is ln((16x^2)/((x+3)^{12)})

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simplify 4ln(2)+2ln(x)-12ln(x+3)

simplify

4 ln (2) + 2 ln (x) - 12 ln (x + 3)

ln (\frac{16 x ^{2}}{( x + 3 ) ^{12}})

Solution steps

4 ln (2) + 2 ln (x) - 12 ln (x + 3)

Apply log rule:

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

4 ln (2) = ln (2^{4})

= ln (2^{4}) + 2 ln (x) - 12 ln (x + 3)

Apply log rule:

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

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

= ln (2^{4}) + ln (x^{2}) - 12 ln (x + 3)

Apply log rule:

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

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

= ln (2^{4} x^{2}) - 12 ln (x + 3)

2^{4} = 16

= ln (16 x^{2}) - 12 ln (x + 3)

Apply log rule:

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

12 ln (x + 3) = ln ((x + 3)^{12})

= ln (16 x^{2}) - ln ((x + 3)^{12})

Apply log rule:

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

ln (16 x^{2}) - ln ((x + 3)^{12}) = ln (\frac{16 x ^{2}}{( x + 3 ) ^{12}})

= ln (\frac{16 x ^{2}}{( x + 3 ) ^{12}})

ln (13) - 2 (ln (4) + ln (32))

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

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

lo g_{a} (5) + lo g_{a} (4)

ln (\frac{4}{k})

What is 4ln(2)+2ln(x)-12ln(x+3) ?
The solution to 4ln(2)+2ln(x)-12ln(x+3) is ln((16x^2)/((x+3)^{12)})