If \(9^{x} - 9^{x-1} = 72\), then the value of \(\frac{2x - 1}{2x + 3}\) is:
\(\frac{3}{7}\)
Take out the common factor \(9^{x-1}\) from the left side: \(9^{x} - 9^{x-1} = 9^{x-1}(9 - 1)\).
So \(9^{x-1} \times 8 = 72\), giving \(9^{x-1} = 9\).
Therefore \(x - 1 = 1\), so \(x = 2\).
Substitute \(x = 2\) into the expression: \(\frac{2x - 1}{2x + 3} = \frac{2(2) - 1}{2(2) + 3} = \frac{3}{7}\).
Hence, the required value is \(\frac{3}{7}\).
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Important Questions from Algebra
If 2x – y = 2 and xy = \(\frac{3}{2}\) , then what is the value of x 3– \(\frac{{{y^3}}}{8}\) ?
If (10a 3+ 4b 3) : (11a 3- 15b 3) = 7 : 5, then (3a + 5b) : (9a - 2b) =?
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The value of:
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If (x + y) 3+ 27(x - y) 3= (Ax - 2y)(Bx 2+ Cxy + 13y 2), then the value of A - B - C is:
