8^x-1=64

To solve the equation \( 8^{x-1} = 64 \), we start by rewriting both sides of the equation with the same base.

Notice that:

• \( 8 \) can be expressed as \( 2^3 \), so \( 8^{x-1} = (2^3)^{x-1} = 2^{3(x-1)} \).
• \( 64 \) can be expressed as \( 2^6 \).

Now, we can rewrite the equation:

\[ 2^{3(x-1)} = 2^6 \]

Since the bases are the same, we can set the exponents equal to each other:

\[ 3(x-1) = 6 \]

Now, solve for \( x \):

1. Distribute the 3: \[ 3x - 3 = 6 \]

2. Add 3 to both sides: \[ 3x = 9 \]

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

Thus, the solution is:

\[ \boxed{3} \]