Solve for x 4^x=256

Problem

4^x=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 4^1=4 4^2=16 4^3=64 and 4^4=256

4. Substitute 4^4 for 256 in the original equation.

4^x=4^4

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

x=4

Final Answer

x=4

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