Answer:
The single logarithm is ㏒2[x³/(3/x+4)] ⇒ 1st answer
Explanation:
* Lets revise some rules of the logarithmic functions
- log(a^n) = n log(a)
- log(a) + log(b) = log(ab)
- log(a) - log(b) = log(a/b)
* Lets solve the problem
∵ 3㏒2(x) - {㏒2(3) - ㏒2(x + 4)} ⇒ we want to make it single logarithm
# 3㏒2(x) = ㏒2(x³)
# ㏒2(3) - ㏒2(x + 4) = ㏒2[3/(x + 4)]
∴ 3㏒2(x) - {㏒2(3) - ㏒2(x + 4)} = ㏒2(x³) - ㏒2[3/(x + 4)]
∵ ㏒2(x³) - ㏒2[3/(x + 4)] = ㏒2[x³ ÷ 3/(x + 4)]
∴ 3㏒2(x) - {㏒2(3) - ㏒2(x + 4)} = ㏒2[x³/(3/x+4)]
* The single logarithm is ㏒2[x³/(3/x+4)]