https://file.aiquickdraw.com/mathbot/file/1729992245789rq3qmg6v.jpg

Let's solve the equation provided:  
\[
10^{x + 9} = 10^{6x - 7}
\]

### Step-by-Step Solution:
Since both sides have the same base \(10\), we can apply the **like bases property**. This property states that if:
\[
a^m = a^n, \quad \text{then} \quad m = n
\]
So, we equate the exponents:
\[
x + 9 = 6x - 7
\]

### Step 1: Rearrange terms to isolate \(x\).
\[
9 + 7 = 6x - x
\]
\[
16 = 5x
\]

### Step 2: Solve for \(x\).
\[
x = \frac{16}{5}
\]

### Final Answer:
\[
x = \frac{16}{5} \approx 3.2
\]

Would you like more details, or do you have any questions?

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Here are 5 related questions for further practice:
1. What is the general form of the like bases property?
2. How do we solve equations with different bases, like \(2^{x + 1} = 8^{2x}\)?
3. What happens when the equation has logarithms, such as \( \log(10^{x + 5}) = 3\)?
4. How would you solve \(10^{x - 3} = 0.01\)?
5. Can this method be applied to solve exponential inequalities, such as \(10^{x + 2} < 10^{5x - 4}\)?

**Tip:** Always ensure the bases are the same before equating exponents when using the like bases property.

Use the like bases property to solve the equation: 10^(x + 9) = 10^(6x - 7).

Learn to solve the exponential equation 10^(x + 9) = 10^(6x - 7) using the like bases property. This solution provides a step-by-step guide to equating exponents and solving for x, ideal for students in Grades 8-10.

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