10 points for those who explain this to me clearly?

Question

rewrite ln 7 + ln x +5 ln (x^2+9) as a single logarithm ln A
please tell me how to do it i mean explain it to me please because i dunno how to do it

Answer 1

There's an identity in logs
that goes like that
lna+lnb=ln(a*b)
or even better
lna +lnb+lnc=ln(a*b*c)
Another identity says
k*lna=lna^k. So
ln7+lnx+5ln(x^2+9)=
ln7+lnx+ln(x^2+9)^5=
ln[7*x*(x^2+9)^5]

Answer 2

This problem involves the properties of logarithms, which are
ln (a*b) = ln a + ln b
ln (a/b) = ln a - ln b
ln a^b = b*ln a
ln 1 = 0

So
ln 7 + ln x + 5 ln (x^2+9)
=ln 7 + ln x + ln (x^2+9)^5
= ln (7x*(x^2+9)^5)

Answer 3

Well recall that ln ab = ln a + ln b.
So the first 2 terms become ln 7x.
Next a*ln b= ln (b^a).
So 5 ln(x²+9) = ln(x²+9)^5.
Now combine this with the first answer to get
ln( 7x*(x²+9)^5).