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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

User Imprezzeb
by
8.1k points

2 Answers

1 vote

Answer: B ON EDG 2021

Explanation:

Easy work :)

User Paul Preibisch
by
8.2k points
2 votes

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.

User Tim Van Dalen
by
8.4k points

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