Question

Which expression is equivalent to log Subscript 12 Baseline (StartFraction one-half Over 8 w EndFraction?

log3 – log(x + 4)
log12 + logx
log3 + log(x + 4)
StartFraction log 3 Over log (x + 4) EndFraction

Answer 1

Answer: B ON EDG 2021

Explanation:

Easy work :)

Answer 2

The options are:

`(A)log_(12)8-log_(12)(1)/(2)+log_(12)w\\(B)log_(12)(1)/(2)-(log_(12)8+log_(12)w)\\(C)log_(12)(1)/(2)-log_(12)8+log_(12)w\\(D)(log_(12)(1)/(2))/(log_(12)8)+log_(12)w`

Answer:

`[B] log_(12)(1)/(2)- (log_(12)8+ log_(12)w).`

Explanation:

Given the expression:

`log_(12)((1)/(2))/(8w)`

Step 1: Apply the division law of logarithm

`log_(x)(a)/(b)= log_x}a- log_(x)b`

Therefore:

`log_(12)((1)/(2))/(8w)= log_(12)(1)/(2)- log_(12){8w}`

STEP 2:Apply the multiplication law of logarithm.

`log_(x)ab= log_(x)a+ log_(x)b`

Therefore:

`log_(12){8w}= log_(12)8+ log_(12)w`

STEP 3: Substitute the result from step 2 into the result from step 1

`log_(12)((1)/(2))/(8w)= log_(12)(1)/(2)- (log_(12)8+ log_(12)w).`

The correct option is B.