Let's solve the equation:

\[
16^{2x-1} = 64
\]

### Step 1: Express both sides as powers of 2

We know:
\[
16 = 2^4 \quad \text{and} \quad 64 = 2^6
\]

So the equation becomes:
\[
(2^4)^{2x-1} = 2^6
\]

### Step 2: Simplify the powers

When raising a power to another power, you multiply the exponents:
\[
2^{4(2x-1)} = 2^6
\]

This simplifies to:
\[
2^{8x-4} = 2^6
\]

### Step 3: Set the exponents equal to each other

Since the bases are the same (both powers of 2), we can set the exponents equal:
\[
8x - 4 = 6
\]

### Step 4: Solve for \(x\)

Add 4 to both sides:
\[
8x = 10
\]

Now, divide by 8:
\[
x = \frac{10}{8} = \frac{5}{4}
\]

### Final Answer:
\[
x = \frac{5}{4}
\]

Would you like any additional details or further clarification on this?

Here are 5 related questions you might find interesting:
1. What happens if \(16^{2x+1} = 64\) instead?
2. How would you solve \(9^{x+2} = 81\)?
3. Can you express 32 as a power of 2 and solve \(32^{3x} = 64\)?
4. How would you solve an equation involving logarithms, such as \(\log_2(16^{2x-1}) = 6\)?
5. What if the equation was \(16^{2x-1} = 128\)?

**Tip:** Always express numbers in the same base (e.g., powers of 2) when solving exponential equations—it simplifies the solution process.

Learn how to solve the exponential equation 16^(2x-1) = 64 by expressing both sides as powers of 2. This solution walks through key concepts such as the laws of exponents and setting exponents equal. Suitable for students in Grades 9-10.

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