Evaluate log of 1/( square root of 10)

Problem

(log_)(1/√(,10))

Solution

1. Identify the base of the logarithm. Since no base is specified, we assume the common logarithm with base 10

(log_10)(1/√(,10))

2. Rewrite the square root as a fractional exponent.

√(,10)=10(1/2)

3. Apply the rule for negative exponents to move the term from the denominator to the numerator.

1/(10(1/2))=10(−1/2)

4. Substitute this expression back into the logarithm.

(log_10)(10(−1/2))

5. Use the property of logarithms (log_b)(bx)=x to evaluate the expression.

−1/2

Final Answer

(log_)(1/√(,10))=−1/2

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