Transcript text: Find the logarithm.
\[
\log (1,000)=
\]
Solution
Solution Steps
Step 1: Understanding the Logarithm
The logarithm \(\log_b a\) answers the question, "To what power must \(b\) be raised, to yield \(a\)?". In mathematical terms, if \(\log_b a = x\), then \(b^x = a\).
Step 2: Using Logarithm Properties
We can use the change of base formula to calculate the logarithm for any base. The change of base formula is \(\log_b a = \frac{\log_c a}{\log_c b}\), where \(c\) is a convenient base for calculation, typically \(e\) (natural logarithm) or 10.
Step 3: Direct Calculation for Common Bases or Using Calculators for Arbitrary Bases
Using the natural logarithm for the change of base formula, we calculate \(\log_b a = \frac{\log_e a}{\log_e b}\) = \frac{6.908}{2.303} = 3.
Final Answer:
The value of \(\log_{10} 1000\) rounded to 2 decimal places is 3.