Question

Which expression is equivalent to log Subscript c Baseline StartFraction x squared minus 1 Over 5 x EndFraction?
log Subscript c Baseline x squared minus log Subscript c Baseline 5 x minus 1
2 log Subscript c Baseline x minus (log Subscript c Baseline 5 + log Subscript c Baseline x) minus 1
log Subscript c Baseline (x squared minus 1) minus (log Subscript c Baseline 5 + log Subscript c Baseline x)
2 log Subscript c Baseline x minus log Subscript c Baseline 1 minus log Subscript c Baseline 5 + log Subscript c Baseline x

Answer 1

The equivalent expression is

log_c(x^2 − 1) − (log_c 5 + log_c x).

Reason: log_c((x^2 − 1)/(5x)) = log_c(x^2 − 1) − log_c(5x) = log_c(x^2 − 1) − (log_c 5 + log_c x).