Suppose for some base $b0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$, and $\log _{b} 7=D$. Express the given logarithms in terms of A, B, C, or D.
-$\log _{b}\left(\frac{1}{4}\right)$
A) $2 \mathrm{~A}$
B) $-2 \mathrm{~A}$
C) $-2 B$
D) $2 \mathrm{~B}$

Question

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$, and $\log _{b} 7=D$. Express the given logarithms in terms of A, B, C, or D.
-$\log _{b}\left(\frac{1}{4}\right)$
A) $2 \mathrm{~A}$
B) $-2 \mathrm{~A}$
C) $-2 B$
D) $2 \mathrm{~B}$

Quizplus · Accepted Answer

Using the properties of logarithms, $\log_b\left(\frac{1}{4}\right) = \log_b(4^{-1}) = -1 \cdot \log_b(4) = -1 \cdot 2\log_b(2) = -2A$.

Suppose for Some Base b>0(b≠1)b>0(b \neq 1)b>0(b=1) That log⁡b2=A,log⁡b3=B,log⁡b5=C\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=Clogb​2=A,logb​3=B,logb​5=C

Suppose for Some Base $b>0(b \neq 1)$ That $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$