Evaluate log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\)
A
-1 1\(\frac{1}{2}\)
B
-1
C
1
D
5
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\)
= log \(_2\) 2\(^3\) – log\(_3\) 9\(^{-1}\)
= log\(_2\) 2\(^3\) – log\(_3\) 3\(^{-2}\)
Based on law of logarithm
= 3 log\(_2\) 2 – (-2 log\(_3\) 3)
But log\(_2\) 2 = 1,
log\(_3\) 3 = 1
So, = 3 + 2
= 5
Source: Myschool Past Questions Archive (Record #47571)