SOLUTION: Oh this logarithm problems are killing me :) Can you help! Write hte logarithm of a single expression: log[b]6x+4(log[b]x-log[b]y) (A) log[b] 6x^5/y^4 (B) log [b] 24x^2/y

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Oh this logarithm problems are killing me :) Can you help! Write hte logarithm of a single expression: log[b]6x+4(log[b]x-log[b]y) (A) log[b] 6x^5/y^4 (B) log [b] 24x^2/y       Log On


   



Question 31666: Oh this logarithm problems are killing me :)
Can you help! Write hte logarithm of a single expression:
log[b]6x+4(log[b]x-log[b]y)
(A) log[b] 6x^5/y^4
(B) log [b] 24x^2/y
(C) log [b] 10x/4y
(D) none of these.
Do we even consider the "B" in this expression?

Found 2 solutions by mukhopadhyay, MathTherapy:
Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
log[b]6x+4(log[b]x-log[b]y)
= log[b]6x + 4log[b]x - 4log[b]y
= log[b]6x + log[b]x^4 - log[b]y^4
= log[b](6x*x^4/y^4)
= log[b](6x^5/y^4)
The correct option for the answer is A. When you send "Thank You" message, would you please indicate the grade level that covers such type of logarithmic problems? Thanks

Answer by MathTherapy(10704) About Me  (Show Source):
You can put this solution on YOUR website!
Oh this logarithm problems are killing me :)
Can you help! Write hte logarithm of a single expression: 
log[b]6x+4(log[b]x-log[b]y)

(A) log[b] 6x^5/y^4

(B) log [b] 24x^2/y

(C) log [b] 10x/4y

(D) none of these.

Do we even consider the "B" in this expression?

log[b]6x+4(log[b]x-log[b]y)
log+%28b%2C+%286x%29%29+%2B+4+%28log+%28b%2C+%28x%29%29+-+log+%28b%2C+%28y%29%29%29
log+%28b%2C+%286x%29%29+%2B+4%2Alog+%28b%2C+%28x%29%29+-+4%2Alog+%28b%2C+%28y%29%29%29 --- Distributing
log+%28b%2C+%286x%29%29+%2B+log+%28b%2C+%28x%29%5E4%29+-+log+%28b%2C+%28y%5E4%29%29%29 ---- Applying c%2Alog+%28d%2C+%28e%29%29 = log+%28d%2C+%28e%5Ec%29%29
log+%28b%2C+%28%286x+%2A+x%5E4%29%2Fy%5E4%29%29 --- Applying log+%28c%2C+%28d%29%29+%2B+log+%28c%2C+%28e%29%29+=+log+%28c%2C+%28d%2Ae%29%29 and log+%28c%2C+%28d%29%29+-+log+%28c%2C+%28e%29%29+=+log+%28c%2C+%28d%2Fe%29%29


Do we even consider the "B" in this expression? 
Don't even consider B or C, as they obviously DO NOT MAKE SENSE. CHOICE D, obviously, is NOT correct either.