Evaluate log base 2 of 8^(1/2)

Problem

(log_2)(8(1/2))

Solution

1. Apply the power rule for logarithms, which states that (log_b)(xp)=p*(log_b)(x)

(log_2)(8(1/2))=1/2*(log_2)(8)

2. Rewrite the argument 8 as a power of the base 2.

8=2

3. Substitute the power back into the logarithmic expression.

1/2*(log_2)(2)

4. Apply the power rule again to the term (log_2)(2)

1/2⋅3*(log_2)(2)

5. Simplify using the property that (log_b)(b)=1

3/2⋅1=3/2

Final Answer

(log_2)(8(1/2))=3/2

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