Suppose for some base b 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms
in terms of A, B, C, or D.
-$\log _ { b } 6$
A) $6 \mathrm {~A}$
B) $- 6 \mathrm {~A}$
C) $\mathrm { A } + \mathrm { C }$
D) $\mathrm { A } + \mathrm { B }$

Question

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms
in terms of A, B, C, or D.
-$\log _ { b } 6$
A) $6 \mathrm {~A}$
B) $- 6 \mathrm {~A}$
C) $\mathrm { A } + \mathrm { C }$
D) $\mathrm { A } + \mathrm { B }$

Quizplus · Accepted Answer

$\log_b 6$ can be expressed as $\log_b (2 \cdot 3)$, which simplifies to $\log_b 2 + \log_b 3$ using the logarithm product rule. Substituting the given values, this becomes $A + B$.

Suppose for Some Base B > 0 (B ≠ 1) log⁡b6\log _ { b } 6logb​6

Suppose for Some Base B > 0 (B ≠ 1) $\log _ { b } 6$