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
The difference between the two positive numbers x and y where x > y, is 25% of x. If the value of y is 15, then the value of x is:
If p2 + q2 - r2 = 0, then the value of (p6 + q6 - r6) ÷ p2q2r2 is:
If √2 + √x = √3, then the value of x is equal to:
The sum of two numbers is 20 and their difference is 2.5. Ratio of these numbers will be:
If \(\rm \frac{\sqrt{19 - x \sqrt{12}}}{1} = \sqrt 4 - \sqrt 3\) then the value of x is equal to:
