Find the value of $\log _ { b } \left( \frac { 49 } { 4 } \right)$, given that $\log _ { b } 4 = 1.266$ and $\log _ { b } 7 = 1.777$.
A) $2.288$
B) $1.892$
C) $4.820$
D) $0.511$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can express $\log_b\left(\frac{49}{4}\right)$ as $\log_b(49) - \log_b(4)$. Given $\log_b(4) = 1.266$ and $\log_b(7) = 1.777$, we can find $\log_b(49)$ by recognizing that $49 = 7^2$, so $\log_b(49) = 2\log_b(7) = 2 \times 1.777 = 3.554$. Therefore, $\log_b\left(\frac{49}{4}\right) = 3.554 - 1.266 = 2.288$.

Find the Value Of log⁡b(494)\log _ { b } \left( \frac { 49 } { 4 } \right)logb​(449​)

Find the Value Of $\log _ { b } \left( \frac { 49 } { 4 } \right)$