write as a snigle logarithm: 6 log b x - 8 log b y?

Question

answer (A) logb(6x/8y) (B) logb(x^6-y^8) (C) logb(68xy) (D) logb(X^6y^8)

Answer 1

There is no correct answer given.

6 log b x - 8 log b y
= log b x^6 - log b y^8
= log b (x^6 / y^8)

Answer 2

I assume that b is the base so really doesn't play much of a part in combining the terms.
When dealing with log, the first step is to move any coefficients (the non-variable numbers that might be in front of the log) to inside the log. when you have alogx, the a becomes the exponent of x. so alogx = log(x^a).
Step 2: When you have two (or more) logs of similar base (which you do since they both are base b) then adding and subtracting them is easy. When you subtract them you divide the terms and when you add them you multiply the terms. for example, log x - log y = log (x/y).

Answer 3

6log(b)x - 8log(b)y
log(b)(x^6) - log(b)(y^8)
log(b)((x^6)/(y^8))

ANS : log(b)((x^6)/(y^8))

so according to your problem, none of them are the answers.

unless you change the - in B to /

if it had been 6log(b)x + 8log(b)y, then D would had been correct.