If $27^{x+2} \div 9^{x+1} = 3^{2x}$, find x

Assessment: JAMB UTME - Mathematics - 2012 Subject: General Mathematics

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$27^{x + 2} \div 9^{x + 1} = 3^{2 x}$
Reduce 27 and 9 to have the same base as 3
$3^{3 (x + 2)} \div 3^{2 (x + 1)} = 3^{2 x}$
Note, - is ÷ and + is × for powers of indices of the same bases.
$3^{3 (x + 2) - 2 (x + 1)} = 3^{2 x}$
Equating the exponentials
$3 (x + 2) - 2 (x + 1) = 2 x$
Clear brackets
$3 x + 6 - 2 x - 2 = 2 x$
Collect like terms
$3 x - 2 x - 2 x = - 6 + 2$
$x - 2 x = - 4$
$- x = - 4$
Divide both sides by $-$
$x = 4$
Answer is B

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If \(27^{x+2} \div 9^{x+1} = 3^{2x}\), find x

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If \(27^{x+2} \div 9^{x+1} = 3^{2x}\), find x

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