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/(xa)=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)(bx)=x to evaluate the expression.

−1/2

Final Answer

(log_3)(1/√(,3))=−1/2

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