If \(243^{3x}=27^{(4x-1)}\), then the value of \(4^x\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{1}{4}\)
Both 243 and 27 are powers of 3. Writing the two sides with the same base, the powers must be equal.
\(243=3^5\) and \(27=3^3\), so \(3^{15x}=3^{3(4x-1)}=3^{12x-3}\)
Equating the powers: \(15x=12x-3\), so \(x=-1\)
So the value asked for is \(4^x=4^{-1}=\frac{1}{4}\)