If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
- \(-\frac{5}{8}\)
- \(-\frac{3}{4}\)
- \(\frac{3}{4}\)
-
\(-\frac{5}{8}\)
The correct answer is: D
Explanation
\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)
\((\frac{1}{9})^{2x-1} = (\frac{1}{9})^{2(2-3x)}\)
\((\frac{1}{9})^{2x-1} = (\frac{1}{9})^{4-6x}\)
Since the bases are equal, powers can be equated
= 2x - 1 = 4 - 6x
= 2x + 6x = 4 + 1
= 8x = 5
\(\therefore x = \frac{5}{8}\)