natural log question?

Question

3lnx - ln3x + ln(12x^2)

explain how to do this please?

Answer 1

2 ln x + ln (12x²)
ln x² + ln (12x²)
ln 12x^4
4 ln 12x

Answer 2

3lnx - ln3x + ln(12x^2)


alnb = ln(b^a)
ln(ab) = ln(a) + ln(b)
ln(a/b) = ln(a) -ln(b)

we will use these formulas to simplify the expression 3lnx - ln3x + ln(12x^2)


3 ln(x) = ln( x^3)

we get:
ln{(x^3)(12x^2)/(3x)} = ln{(12x^4)/3}

= ln(4) + 4 ln(x)

Answer 3

you know that ln(x*y)=lnx+lny
ln(x/y)=lnx-lny
and klna=ln(x^k) for all positive nambers x and y,
and every real number k

so lnx(12x^2)=ln12+lnx^2=ln12+2lnx
and ln3x=ln3+lnx
so 3lnx - ln3x + ln(12x^2)=
=3lnx-ln3-lnx+ln12+2lnx=
=4lnx+ln(12/3)=4lnx+ln4=
=lnx^4+ln4-ln(4x^4)

Answer 4

it is tough.