Question

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

Answer 1

B on edge

Explanation:

Answer 2

`\log_84+\log_8a+\log_8(b-4)-4\log_8c`.

Explanation:

The given expression is

`\log_84a\left((b-4)/(c^4)\right)`

Using the properties of logarithm, we get

`\log_84+\log_8a+\log_8\left((b-4)/(c^4)\right)`
`[\because \log_a mn=\log_a m+\log_a n]`

`\log_84+\log_8a+\log_8(b-4)-\log_8c^4`
`[\because \log_a (m)/(n)=\log_a m-\log_a n]`

`\log_84+\log_8a+\log_8(b-4)-4\log_8c`
`[\because \log_a x^n =n\log_a x]`

Therefore, the required expression is
`\log_84+\log_8a+\log_8(b-4)-4\log_8c`.