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.
-$\log _ { b } 125$
A) $2 \mathrm { C }$
B) $2 \mathrm { D }$
C) $3 C$
D) $3 \mathrm { D }$

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.
-$\log _ { b } 125$
A) $2 \mathrm { C }$
B) $2 \mathrm { D }$
C) $3 C$
D) $3 \mathrm { D }$

Quizplus · Accepted Answer

We know that 125 = 5^3, so we can rewrite $\log _ { b } 125$ as $\log _ { b } 5^3$. Using the property of logarithms that says $\log _ { b } x ^ { n } = n \log _ { b } x $, we can simplify as follows:

$\log _ { b } 5^3 = 3 \log _ { b } 5 = 3C$

Therefore, the answer is C.

Suppose for Some Base B > 0 (B ≠ 1) log⁡b125\log _ { b } 125logb​125

Suppose for Some Base B > 0 (B ≠ 1) $\log _ { b } 125$