If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
FURTHER MATHEMATICS
WAEC 2023
If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
- A. \(-\frac{5}{8}\)
- B. \(-\frac{3}{4}\)
- C. \(\frac{3}{4}\)
- D. \(-\frac{5}{8}\)
Correct Answer: D. \(-\frac{5}{8}\)
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
\(\therefore x = \frac{5}{8}\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *