Question

Which expression is equivalent to log8 4a (b-4/c4)?

Answer 1

the answer:
the main rules of the use of logarithm are

loga[a] = 1
loga[AxB] =loga[A] +loga[B] for all value positive of A and B
loga[A/B] = loga[A] - loga[B] for all value positive of A and B

in our case, log8 4a (b-4/c4)

so it is equivalent to log8 4a + log8(b-4/c4) 
and since loga[A/B] = loga[A] l - oga[B] , log8(b-4/c4)  =log8(b-4) - log8(c4)
 
the possible expression:

log8 4a (b-4/c4) = log8 4a + log8(b-4) - log8(c4)

Answer 2

The equivalent expression of the given logarithmic expresson is $1+log_8a+log_8 (b-4)-log_8 2c^4$.

The given expression is $log_8 [4a ((b-4)/c^4)]$.

Use the basic rules of logarithm to find the equivalent expression.

$log_aa=1\\log(ab)=loga+logb\\log(a/b)=loga-logb\\loga^b=bloga$

Solve the given expression as,

$log_8 [4a ((b-4)/c^4)]=log_8 [8a ((b-4)/2c^4)]\\=log_8 8+log_8a+log_8 (b-4)-log_8 2c^4\\=1+log_8a+log_8 (b-4)-log_8 2c^4$

Therefore, the equivalent expression of the given logarithmic expresson is $1+log_8a+log_8 (b-4)-log_8 2c^4$.

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https://brainly.com/question/23889479