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

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

Question 1 Report

3

4

5

6

Answer Details

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

Related Questions

Everything you need to excel in your exams