Determine the function value.
-Suppose f(x) = loga(x) and f(7) = 2. Find f(343).
A) 3
B) 7
C) 6
D) 12

Question

Quizplus · Accepted Answer

Given that $f(x) = \log_a(x)$ and $f(7) = 2$, this means that $a^2 = 7$. To find $f(343)$, we recognize that $343 = 7^3$. Therefore, $f(343) = \log_a(7^3)$. Using the property of logarithms that $\log_a(b^c) = c \log_a(b)$, we get $f(343) = 3 \log_a(7)$. Since we know $\log_a(7) = 2$, then $f(343) = 3 \times 2 = 6$.

Determine the Function Value