Question

Which expression is equivalent to log Subscript 8 Baseline 4 a (StartFraction b minus 4 Over c Superscript 4 Baseline EndFraction)?

log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c
log Subscript 8 Baseline 4 + log Subscript 8 Baseline a + (log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c)
log Subscript 8 Baseline 4 a + log Subscript 8 Baseline b minus 4 minus 4 log Subscript 8 Baseline c minus 4
log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus log Subscript 8 Baseline 4 c

Answer 1

Its b

Explanation:

edge 2022

Answer 2

`\log _(8) 4+\log _(8) a+\log _(8)(b-4)-4 \log _(8) c`

The equivalent expression is log Subscript 8 Baseline 4 + log Subscript 8 Baseline a + (log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c)

Explanation:

The expression is written as
`\log _(8)\left(4 a\left((b-4)/(c^(4))\right)\right)`

Using the log rule:
`\log _(c)(x y)=\log _(c) x+\log _(c) y`, the expression can be written as,

`\log _(c)(x y)=\log _(c) x+\log _(c) y`

Using the log rule:
`\log _(c)\left((x)/(y)\right)=\log _(c) x-\log _(c) y` , the expression can be written as,

`\log _(8) 4+\log _(8) a+\log _(8)(b-4)-\log _(8) c^(4)`

Since, we know that,
`\log _(a) x^(b)=b \log _(a) x`, the expression is written as,

`\log _(8) 4+\log _(8) a+\log _(8)(b-4)-4 \log _(8) c`

Thus, the equivalent expression is log Subscript 8 Baseline 4 + log Subscript 8 Baseline a + (log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c)