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Xelga [282]
3 years ago
8

Please help me on this one

Mathematics
1 answer:
Aliun [14]3 years ago
6 0

Answer:

The single logarithm is ㏒2[x³/(3/x+4)] ⇒ 1st answer

Step-by-step 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)]

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