solve exponential equation 16=4 raised to (x-1)

To solve the exponential equation \( 16 = 4^{x-1} \), we can follow these steps:

### Step 1: Express 16 as a power of 4
Since \( 16 = 4^2 \), we can rewrite the equation as:
\[
4^2 = 4^{x-1}
\]

### Step 2: Set the exponents equal
Since the bases are the same (both are 4), we can set the exponents equal to each other:
\[
2 = x - 1
\]

### Step 3: Solve for \( x \)
Add 1 to both sides of the equation:
\[
x = 3
\]

### Solution:
The solution to the equation is \( x = 3 \).

Would you like more details on any part of the process? Here are some related questions that could deepen your understanding:

1. How do you solve exponential equations with different bases?
2. What if the bases were not the same? How would you solve the equation?
3. Can you solve an exponential equation using logarithms? How?
4. How does the property of exponents work in equations like this?
5. What are other methods to verify the solution of an exponential equation?

**Tip:** When solving exponential equations, always check if the bases can be rewritten to be the same. This simplifies the process by allowing you to set the exponents equal.

Learn how to solve the exponential equation 16 = 4^(x-1) step-by-step with detailed explanations. This problem involves exponential equations and requires understanding exponential rules and properties. Suitable for Grades 9-12.

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