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
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.
I. x2 – 26x + 165 = 0
II. y2 – 38y + 357 = 0
Factorize the following:
(x 2- 6xy + 9y 2) - 25
If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that
AP = PQ = QB, then the mid point of PQ is
If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?
If 3x + 2y = 15, and xy = 6. Find the value of (3x3/2) + (4y3/9).
