Evaluate log base 3 of 1/( square root of 3)

Problem

(log_3)(1/√(,3))

Solution

1. Rewrite the square root as a fractional exponent using the property √(,x)=x^(1/2)

√(,3)=3^(1/2)

2. Apply the negative exponent rule 1/(x^a)=x^(−a) to move the term to the numerator.

1/(3^(1/2))=3^(−1/2)

3. Substitute this expression back into the logarithm.

(log_3)(3^(−1/2))

4. Use the logarithm power property (log_b)(b^x)=x to evaluate the expression.

−1/2

Final Answer

(log_3)(1/√(,3))=−1/2

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