Evaluate log base 4 of 256

Problem

(log_4)(256)

Solution

1. Identify the base and the argument of the logarithm. The base is 4 and the argument is 256

2. Rewrite the expression as an equation by setting it equal to x

(log_4)(256)=x

3. Convert the logarithmic equation into its equivalent exponential form.

4=256

4. Express the number 256 as a power of 4 by testing integer exponents.

4=4

4=16

4=64

4=256

5. Substitute the power back into the exponential equation.

4=4

6. Solve for x by equating the exponents since the bases are the same.

x=4

Final Answer

(log_4)(256)=4

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