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.
-$\log _{b} 21$
A) $B+D$
B) $\mathrm{B}+\mathrm{C}$
C) $A+B$
D) $A+D$

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.
-$\log _{b} 21$
A) $B+D$
B) $\mathrm{B}+\mathrm{C}$
C) $A+B$
D) $A+D$

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the product rule $\log_b(xy) = \log_b(x) + \log_b(y)$, we can express $\log_b(21)$ as $\log_b(3) + \log_b(7)$, which corresponds to $B + D$.

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 $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$