Evaluate log10(11000)

Sure, let's evaluate $\log_{10}(11000)$ step by step.

1. Understand the logarithm definition: The logarithm $\log_{10}(x)$ is the power to which the base 10 must be raised to obtain the number $x$.

2. Express 11000 in terms of powers of 10: $11000 = 1.1 \times 10^4$

3. Use the properties of logarithms: The logarithm of a product is the sum of the logarithms of the factors. $\log_{10}(11000) = \log_{10}(1.1 \times 10^4)$ $\log_{10}(11000) = \log_{10}(1.1) + \log_{10}(10^4)$

4. Evaluate $\log_{10}(10^4)$: By definition, $\log_{10}(10^4) = 4$ because 10 raised to the power of 4 is 10000. $\log_{10}(10^4) = 4$

5. Evaluate $\log_{10}(1.1)$: This is a bit more complex and typically requires a calculator. However, for the sake of this step-by-step process, let's assume we use a calculator to find: $\log_{10}(1.1) \approx 0.0414$

6. Add the results: $\log_{10}(11000) = \log_{10}(1.1) + \log_{10}(10^4)$ $\log_{10}(11000) \approx 0.0414 + 4$ $\log_{10}(11000) \approx 4.0414$

So, the value of $\log_{10}(11000)$ is approximately 4.0414.