Given that log\(_2a\) = log\(_84\), find a.
A
2\(^{\frac{1}{2}}\)
B
2\(^{\frac{2}{3}}\)
C
4\(^{\frac{2}{3}}\)
D
4\(^{\frac{1}{2}}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
log\(_2a\) = log\(_84\)
Let log\(_84\) = y
Then 4 = 8\(^y\)
2\(^2\) = 2\(^{3y}\)
2 = 3y
y = \(\frac{2}{3}\)
log\(_2a\) = log\(_84\) = \(\frac{2}{3}\)
log\(_2a\) = \(\frac{2}{3}\)
a = 2\(^{\frac{2}{3}}\)
(Note: The logarithm was converted to index form.)
Source: Myschool Past Questions Archive (Record #75800)