https://file.aiquickdraw.com/mathbot/file/1726746278013njy2ex4n.jpg

The equation provided in the image is:

\[
3^{2x - 4} = 3^{5x + 8}
\]

Since the bases on both sides of the equation are the same, we can set the exponents equal to each other:

\[
2x - 4 = 5x + 8
\]

Now, solve for \(x\):

1. Subtract \(2x\) from both sides:
   \[
   -4 = 3x + 8
   \]

2. Subtract 8 from both sides:
   \[
   -12 = 3x
   \]

3. Divide by 3:
   \[
   x = -4
   \]

So, the solution is \(x = -4\).

Would you like more details or have any questions? Here are five related questions for further practice:

1. What happens if the bases of the exponents are not the same?
2. Solve for \(x\): \(4^{x + 2} = 4^{3x - 6}\).
3. How would you solve the equation if it were \(2^{3x - 1} = 8^{2x}\)?
4. What is the general method to solve exponential equations like this?
5. Solve for \(x\): \(7^{x + 1} = 7^{4 - x}\).

**Tip:** When the bases of two exponential expressions are the same, you can simplify by equating their exponents.

Solve the value of x: 3^(2x - 4) = 3^(5x + 8)

Learn how to solve the exponential equation 3^(2x - 4) = 3^(5x + 8) using basic algebraic techniques. The solution involves equating the exponents and solving a simple linear equation. Suitable for students in Grades 9-12.

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