🎥 Watch Video Solution
Q. If \( a^{b^c} = 6561 \), find least value of \( abc \)
(a) 24 (b) 36 (c) 162 (d) none of these
✏️ Solution
\( 6561 = 3^8 \)
So \( a^{b^c} = 3^8 \)
Take smallest base: \( a = 3 \Rightarrow b^c = 8 \)
To minimize \( bc \): \( 8 = 2^3 \Rightarrow b = 2,\ c = 3 \)
\( abc = 3 \cdot 2 \cdot 3 = 18 \)
18 not in options ⇒ answer is none of these
Correct Option: (d) none of these
\( \boxed{18} \)