Solution
The equation on the board is:
4x−1=644^{x – 1} = 64
Step 1: Rewrite both sides using powers of 2.
4=22,64=264 = 2^2,\quad 64 = 2^6
So:
4x−1=(22)x−1=22(x−1)4^{x – 1} = (2^2)^{x – 1} = 2^{2(x – 1)}
Thus:
22(x−1)=262^{2(x – 1)} = 2^6
Step 2: Set exponents equal:
2(x−1)=62(x – 1) = 6 x−1=3x – 1 = 3 x=4x = 4
Step 3: Find 4+x4 + x:
4+x=4+4=84 + x = 4 + 4 = 8
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