Solve for x 4^x=256

Problem

4=256

Solution

1. Identify the base of the exponential expression on the left side, which is 4

2. Rewrite the right side of the equation, 256 as a power of 4 by testing exponents.

3. Calculate the powers of 4 4=4 4=16 4=64 and 4=256

4. Substitute 4 for 256 in the original equation.

4=4

5. Apply the property of equality for exponential functions, which states that if bx=by and b>0,b≠1 then x=y

x=4

Final Answer

x=4

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