Question

What is 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline minus 7 squared) written as a single logarithm?
log Subscript 3 Baseline 2 z
log Subscript 3 Baseline 2 z squared
log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction
log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction

Answer 1

2(log_3 8 + log_3 z) = 2 log_3(8z) = log_3((8z)^2) = log_3(64 z^2).
3^4 - 7^2 = 81 - 49 = 32, so subtracting gives log_3(64 z^2) - log_3 32 = log_3((64 z^2)/32) = log_3(2 z^2).

Answer: log_3(2 z^2) (option 2).