Evaluate log of 1000x

Problem

(log_)(1000*x)

Solution

1. Identify the base of the logarithm. Since no base is explicitly written, it is assumed to be the common logarithm with base 10

2. Apply the product rule for logarithms, which states that (log_b)(M*N)=(log_b)(M)+(log_b)(N)

3. Expand the expression using the product rule.

(log_)(1000*x)=(log_)(1000)+(log_)(x)

4. Evaluate the numerical logarithm by expressing 1000 as a power of 10

1000=10^3

5. Simplify the term (log_)(10^3) using the property (log_b)(b^y)=y

(log_)(10^3)=3

6. Combine the results to find the final expanded form.

Final Answer

(log_)(1000*x)=3+(log_)(x)

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