Provide an appropriate response.
-If $\log _ { \mathrm { b } } 3 = 0.79$ and $\log _ { \mathrm { b } } 5 = 1.16$, find the value of of $\log _ { \mathrm { b } } \frac { 3 } { 125 }$.
A) $- 2.69$
B) $0.14$
C) $- 1.11$
D) $4.27$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\log_b \frac{3}{125}$ can be rewritten as $\log_b 3 - \log_b 125$. Given $\log_b 3 = 0.79$ and knowing $125 = 5^3$, we can find $\log_b 125 = 3\log_b 5 = 3(1.16) = 3.48$. Thus, $\log_b \frac{3}{125} = 0.79 - 3.48 = -2.69$.

Provide an Appropriate Response log⁡b3=0.79\log _ { \mathrm { b } } 3 = 0.79logb​3=0.79

Provide an Appropriate Response $\log _ { \mathrm { b } } 3 = 0.79$