Rewrite the expression as a single logarithm ln A Then the f

Rewrite the expression as a single logarithm ln A. Then the function A=

A. ln (a+b) + 4ln(a-b) -4 ln c

B.ln 4+ 4ln x + 2ln(x^2+8)

Solution

A. ln(a+b) + 4ln(a-b) - 4ln c

We have to use the following log properties

loga + logb= log ab

log a- log b=log a/b

m log n= log n^m

ln(a+b) + ln(a-b)^4 - ln c^4

ln ((a+b)(a-b)^4/c^4)

B. ln4 + 4lnx + 2ln(x^2+8)

ln 4 + lnx^4+ln (x^2+8)^2

ln(4(x^4)(x^2 + 8)^2)