Evaluate log base 3 of square root of 3

Problem

(log_3)(√(,3))

Solution

1. Rewrite the square root using a fractional exponent.

√(,3)=3(1/2)

2. Substitute the exponential form back into the logarithmic expression.

(log_3)(3(1/2))

3. Apply the power property of logarithms, which states (log_b)(xp)=p*(log_b)(x)

1/2*(log_3)(3)

4. Simplify the expression using the identity (log_b)(b)=1

1/2⋅1=1/2

Final Answer

(log_3)(√(,3))=1/2

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