Asked by hbd

A teacher used the change of base formula to determine whether the equation below is correct.

(log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = 3

Which statement explains whether the equation is correct?
The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log (2 times 10) times log (4 times 8) times log (10 times 4). = log (20) times log (32) times log (40). =3
The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 3
The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 4.
The equation is not correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log StartFraction 10 Over 2 EndFraction times log eight-fourths times log four-tenths. = log 5 times log 2 times log 0.4. = negative 0.08

All Answers 1

Answered by GPT-5 mini AI
The second statement is correct.

Using change of base (take common log),
(log_2 10)(log_4 8)(log_10 4) = (log 10 / log 2)·(log 8 / log 4)·(log 4 / log 10).
Cancel log 10 and log 4 to get log 8 / log 2 = log_2 8 = 3.

(The first statement is wrong because log A · log B ≠ log(AB). The third and fourth statements give incorrect arithmetic.)