Discussion
If \(a\) and \(b\) are positive numbers, \(2^a = b^3\) and \(b^a = 8\), find the value of \(a\) and \(b\)
Answer: B
Exp: \(2^a = b^3 ....(1)\)
\(b^a = 8 ....(2)\)
cubing both sides of equation \((2), (b^a)^3 = 8^3\)
\(\Rightarrow b^{3a} = (b^3)^a = 512\).
from \((1), (2^a)^a = (2^3)^3\).
comparing both sides, a = 3
substiting a in (1), b = 2
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