Find each value. If applicable, give an approximation to four decimal places. log 518 - log 342

Verified step by step guidance

1. Recall the logarithmic property that states: \(\log a - \log b = \log \left( \frac{a}{b} \right)\).
2. Apply this property to the given expression: \(\log 518 - \log 342 = \log \left( \frac{518}{342} \right)\).
3. Simplify the fraction inside the logarithm: calculate \(\frac{518}{342}\).
4. Evaluate the logarithm of the simplified fraction using a calculator or logarithm table.
5. If needed, approximate the value to four decimal places.

Key Concepts

Properties of Logarithms

Logarithms have specific properties that simplify expressions, such as the subtraction property: log(a) - log(b) = log(a/b). This allows combining or breaking down logarithmic expressions to make calculations easier.

Evaluating Logarithmic Expressions

To find the value of a logarithmic expression, you may need to rewrite it using properties or convert it to a common base. Understanding how to evaluate or approximate logs, especially with non-standard bases, is essential.

Decimal Approximation of Logarithms

When exact values are not possible, logarithms can be approximated using calculators or tables. Rounding to a specified number of decimal places, such as four, ensures precision and clarity in the final answer.