Problem 62 - College Algebra

Question

Evaluate each expression without using a calculator. $$\log 1000$$

Step-by-Step Solution

Answer

Therefore, the value of \(\log 1000\) is 3.

Step 1: Identify the Base and the Result

Identify the base of the logarithm and the result of the logarithm. In this case, the base is 10 (implicit base of common log) and the result is 1000.

Step 2: Write the Equivalent Exponential Equation

Write the equivalent exponential equation from the log equation. The general form is \(b^n=a\), so in this situation, it's \(10^n = 1000\).

Step 3: Find the Exponent

Find the exponent 'n' such that \(10^n = 1000\). In this case, since \(10^3 = 1000\), 'n' should be 3.