Question

Rewrite the following as a single logarithm. Please show ALL work! log₃2+2log₃4

Answer 1

Note: All logs used in the steps below are base 3 logs

I'll use the following log rules
Rule 1: log(x)+log(y) = log(x*y)
Rule 2: y*log(x) = log(x^2)


Using those log rules, we get...
log(2) + 2*log(4)
log(2) + log(4^2) ... using rule 2
log(2) + log(16)
log(2*16) ... using rule 1
log(32)

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Final Answer: $\log_{3}(32)$