Simplify/Condense log of 10000x

Problem

(log_)(10000*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)

(log_)(10000*x)=(log_)(10000)+(log_)(x)

3. Evaluate the numerical logarithm by expressing 10000 as a power of 10 Since 10000=10 then (log_)(10)=4

(log_)(10000)=4

4. Substitute the value back into the expression to reach the simplest form.

4+(log_)(x)

Final Answer

(log_)(10000*x)=4+(log_)(x)

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