Let's solve the equation \( 4^x + 4^x = 16 \).

1. Combine the terms on the left side:
   \[
   2 \cdot 4^x = 16
   \]

2. Divide both sides by 2 to isolate \( 4^x \):
   \[
   4^x = \frac{16}{2} = 8
   \]

3. Express 8 as a power of 4 to see if it matches \( 4^x \):
   \[
   8 = 2^3
   \]
   However, 8 cannot be expressed as a power of 4 using integer exponents.

4. Alternatively, recognize that we need to solve this equation differently. Since \( 4^x = 2^{2x} \), the equation becomes:
   \[
   2^{2x} = 8
   \]
   Now express 8 as a power of 2:
   \[
   8 = 2^3
   \]
   So, we have:
   \[
   2^{2x} = 2^3
   \]

5. Since the bases are equal, set the exponents equal:
   \[
   2x = 3
   \]

6. Solve for \( x \):
   \[
   x = \frac{3}{2} = 1.5
   \]

Therefore, the solution is \( x = 1.5 \).

Would you like more details or have any questions? Here are some related questions:

1. How do you solve exponential equations with the same base?
2. What is the property of exponents that allows you to set exponents equal when the bases are the same?
3. How do you convert a number into a power of another base?
4. What are the steps to solve equations involving exponents?
5. Can exponential equations have non-integer solutions?
6. How do you check if your solution to an exponential equation is correct?
7. What is the general form of an exponential function?
8. How can logarithms be used to solve exponential equations?

**Tip:** When solving exponential equations, it's often useful to express all terms with the same base to simplify the comparison of exponents.

Learn how to solve the exponential equation 4^x + 4^x = 16 step-by-step. Understand the properties of exponents and exponentiation rules applied in solving equations. Suitable for high school students studying algebra and exponential functions.

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