If 3x-1 + 3x+3 + 3x-2 = 741, then find the value of x.

Concept

Law of Indices — for any base A: Am+n = Am × An, Am-n = Am ÷ An, and A-m = 1/Am.

Application

1. Rewrite each term using the laws above: 3x-1 + 3x+3 + 3x-2 = 741 becomes 3x × 3-1 + 3x × 33 + 3x × 3-2 = 741.

2. Factor out the common term 3x: 3x × (1/3 + 27 + 1/9) = 741.

3. Combine the bracket over the common denominator 9: 1/3 + 27 + 1/9 = 3/9 + 243/9 + 1/9 = 247/9, so 3x × 247/9 = 741.

4. Solve for 3x: 3x = 741 × 9/247 = 27.

5. Write 27 as a power of 3: 3x = 33, so x = 3.

Cross-check

Substitute x = 3 back into the original equation: 32 + 36 + 31 = 9 + 729 + 3 = 741, which confirms the answer.