Question

Expand the following logarithmic expression.

log Subscript 5 Baseline (8 StartFraction StartRoot t EndRoot Over v EndFraction)

log Subscript 5 Baseline 8 + 2 log Subscript 5 Baseline t minus log Subscript 5 Baseline v

log Subscript 5 Baseline 8 + log Subscript 5 Baseline one-half t minus log Subscript 5 Baseline v

One-half log Subscript 5 Baseline 8 + one-half log Subscript 5 Baseline t minus one-half log Subscript 5 Baseline v

log Subscript 5 Baseline 8 + one-half log Subscript 5 Baseline t minus log Subscript 5 Baseline v

Answer 1

log_5(8 * sqrt(t) / v) = log_5(8) + log_5(t^{1/2}) - log_5(v) = log_5(8) + (1/2) log_5(t) - log_5(v).

So the correct choice is: log_5 8 + one-half log_5 t − log_5 v.