Solve for x: ﻿9 to the power of 2 x plus 5 end exponent equals 9 to the power of 10

We are given the equation:

\[
9^{(2x + 5)} = 9^{10}
\]

Since the bases (9) are the same, we can set the exponents equal to each other:

\[
2x + 5 = 10
\]

Now, solve for \(x\):

1. Subtract 5 from both sides:
   \[
   2x = 10 - 5
   \]
   \[
   2x = 5
   \]

2. Divide both sides by 2:
   \[
   x = \frac{5}{2}
   \]
   \[
   x = 2.5
   \]

Thus, the solution is \(x = 2.5\).

Would you like further details or have any questions?

Here are some related questions to practice:
1. Solve for \(x\): \(9^{(3x + 2)} = 9^{11}\)
2. Solve for \(x\): \(5^{(x + 4)} = 5^9\)
3. Solve for \(x\): \(7^{(2x - 3)} = 7^5\)
4. Solve for \(x\): \(4^{(x + 6)} = 4^8\)
5. Solve for \(x\): \(10^{(x + 1)} = 10^6\)

**Tip:** When dealing with exponential equations with the same base, you can directly equate the exponents.

Learn how to solve the exponential equation 9^(2x + 5) = 9^10 with a step-by-step solution. This problem involves key algebraic concepts such as equating exponents when the bases are the same. Suitable for students in Grades 8-10.

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