Simplify/Condense log of 1/( square root of 1000)

Problem

(log_)(1/√(,1000))

Solution

1. Rewrite the square root as a fractional exponent.

√(,1000)=1000(1/2)

2. Express the fraction using a negative exponent.

1/(1000(1/2))=1000(−1/2)

3. Substitute the power back into the logarithm.

(log_)(1000(−1/2))

4. Apply the power rule for logarithms, (log_)(ab)=b*(log_)(a)

−1/2*(log_)(1000)

5. Evaluate the common logarithm (base 10) of 1000, since 10=1000

(log_)(1000)=3

6. Multiply the resulting values to find the final simplified form.

−1/2⋅3=−3/2

Final Answer

(log_)(1/√(,1000))=−3/2

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