Evaluate \(\frac{log_5 (0.04)}{log_3 18 - log_3 2}\)
A
1
B
-1
C
\(\frac{2}{3}\)
D
-\(\frac{2}{3}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{log_5 0.04}{log_3 18 - log_3 2}\)
= \(\frac{log_5 0.04}{log_3(\frac{18}{2})}\)
= \(\frac{log_5 0.04}{log_3 9}\)
= \(\frac{-2}{2}\)
= -1
Let log5 0.04 = x
5x = 0.04
x = \(\frac{4}{100}\) = 5\(^{-2}\)
Let log\(_3\) 9 = z
3\(^2\) = 3\(^z\)
z = 3
Source: Myschool Past Questions Archive (Record #30978)