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.
-$\log _ { \mathrm { b } } 14$
A) $B + C$
B) $C + D$
C) $A + B$
D) $A + D$

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.
-$\log _ { \mathrm { b } } 14$
A) $B + C$
B) $C + D$
C) $A + B$
D) $A + D$

Quizplus · Accepted Answer

We can use the property that $\log_b (mn) = \log_b m + \log_b n$ to write $14 = 2\cdot7$. Then, using the given logarithms, we get: $$\log_b 14 = \log_b (2\cdot7) = \log_b 2 + \log_b 7 = A + D.$$ Therefore, the answer is D.

Suppose for Some Base B > 0 (B ≠ 1) log⁡b14\log _ { \mathrm { b } } 14logb​14

Suppose for Some Base B > 0 (B ≠ 1) $\log _ { \mathrm { b } } 14$