Question

Which expression is equivalent to log Subscript 12 Baseline StartFraction x Superscript 4 Baseline StartRoot x cubed minus 2 EndRoot Over (x + 1) Superscript 5 Baseline EndFraction?
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline StartFraction x cubed Over 2 EndFraction minus 5 log Subscript 12 Baseline 1
log Subscript 12 Baseline 4 x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x) + 1
4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)

Answer 1

4 log_12 x + (1/2) log_12 (x^3 − 2) − 5 log_12 (x + 1)

Reason: log_12[x^4 * (x^3 − 2)^{1/2} / (x+1)^5] = 4 log_12 x + (1/2) log_12(x^3 − 2) − 5 log_12(x+1).