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Q. If \( 8^{x+1} = 64 \), find \( 3^{2x+1} \)
(a) 1 (b) 3 (c) 9 (d) 27
тЬПя╕П Solution
\( 8 = 2^3,\quad 64 = 2^6 \)
\( (2^3)^{x+1} = 2^6 \)
\( 2^{3(x+1)} = 2^6 \)
\( 3(x+1) = 6 \)
\( x+1 = 2 \)
\( x = 1 \)
\( 3^{2x+1} = 3^{2(1)+1} \)
\( = 3^3 \)
\( = 27 \)
Correct Option: (d) 27
\( \boxed{27} \)