Question

`9^(2x - 1) = 27^(x + 2)`

∴ x = ______.

पर्याय

• 7

• 8

• 6

• –1

Answer 1

∴ x = 8.

Explanation:

We are given the equation:

`9^((2x - 1)) = 27^((x + 2))`

To solve for x, we will express both sides with the same base.

1. Rewrite 9 and 27 as powers of 3:

• 9 = 3²
• 27 = 3³

So, the equation becomes:

`(3^2)^((2x - 1)) = (3^3)^((x + 2))`

2. Simplify the exponents:

• `(3^2)^((2x - 1)) = 3^(2(2x - 1)) = 3^((4x - 2))`
• `(3^3)^((x + 2)) = 3^(3(x + 2)) = 3^((3x + 6))`

Now the equation becomes:

`(3)^((4x - 2)) = (3)^((3x + 6))`

3. Since the bases are the same, equate the exponents:

4x – 2 = 3x + 6

4. Solve for x:

Subtract 3x from both sides:

x – 2 = 6

Add 2 to both sides:

x = 8