Find each value. If applicable, give an approximation to four decimal places. log(387 $\times$ 23)

Verified step by step guidance

1. Recall the logarithm property that states \( \log(a \times b) = \log a + \log b \). This allows us to break down the logarithm of a product into the sum of logarithms.
2. Apply the property to the given expression: \( \log(387 \times 23) = \log 387 + \log 23 \).
3. Find the logarithm of each number separately: calculate \( \log 387 \) and \( \log 23 \). Depending on the base of the logarithm (commonly base 10), you can use a calculator or logarithm tables for these values.
4. Add the two logarithm values obtained in the previous step: \( \log 387 + \log 23 \).
5. If required, approximate the final sum to four decimal places to get the answer.

Key Concepts

Properties of Logarithms

Logarithms have specific properties that simplify calculations, such as the product rule: log(a * b) = log(a) + log(b). This allows breaking down complex logarithmic expressions into sums of simpler logs, making evaluation easier.

Evaluating Logarithms

Evaluating a logarithm means finding the exponent to which the base must be raised to get the given number. For common logarithms (base 10), this often involves using a calculator or logarithm tables to find approximate decimal values.

Rounding and Approximation

When exact values are not possible or practical, logarithmic results are approximated to a specified number of decimal places. Rounding to four decimal places means adjusting the number so that only four digits appear after the decimal point, ensuring clarity and precision.