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Solution

The equation on the board is:

4x−1=644^{x – 1} = 644x−1=64

Step 1: Rewrite both sides using powers of 2.

4=22,64=264 = 2^2,\quad 64 = 2^64=22,64=26

So:

4x−1=(22)x−1=22(x−1)4^{x – 1} = (2^2)^{x – 1} = 2^{2(x – 1)}4x−1=(22)x−1=22(x−1)

Thus:

22(x−1)=262^{2(x – 1)} = 2^622(x−1)=26

Step 2: Set exponents equal:

$$2(x-1)=6$$ $$x-1=3$$ $$x=4$$

Step 3: Find $4+x$:

$$4+x=4+4=8$$