What is ln(2)+2ln(x)+6ln(x^2+3) ?

The solution to ln(2)+2ln(x)+6ln(x^2+3) is ln(2x^2(x^2+3)^6)

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simplify ln(2)+2ln(x)+6ln(x^2+3)

simplify

ln (2) + 2 ln (x) + 6 ln (x^{2} + 3)

ln (2 x^{2} (x^{2} + 3)^{6})

Solution steps

ln (2) + 2 ln (x) + 6 ln (x^{2} + 3)

Apply log rule:

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

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

= ln (2) + ln (x^{2}) + 6 ln (x^{2} + 3)

Apply log rule:

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

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

= ln (2 x^{2}) + 6 ln (x^{2} + 3)

Apply log rule:

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

6 ln (x^{2} + 3) = ln ((x^{2} + 3)^{6})

= ln (2 x^{2}) + ln ((x^{2} + 3)^{6})

Apply log rule:

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

ln (2 x^{2}) + ln ((x^{2} + 3)^{6}) = ln (2 x^{2} (x^{2} + 3)^{6})

= ln (2 x^{2} (x^{2} + 3)^{6})

ln (x + 6) + ln (x + 7) + ln (6)

ln (e^{2}) + ln (2 e)

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

ln (\frac{1}{10}) + ln (e^{3})

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

What is ln(2)+2ln(x)+6ln(x^2+3) ?
The solution to ln(2)+2ln(x)+6ln(x^2+3) is ln(2x^2(x^2+3)^6)