Find each value. If applicable, give an approximation to four decimal places. log 387 + log 23

Verified step by step guidance

1. Recall the logarithm property that states: \(\log a + \log b = \log (a \times b)\). This means you can combine the sum of two logarithms into the logarithm of the product of their arguments.
2. Apply this property to the given expression: \(\log 387 + \log 23 = \log (387 \times 23)\).
3. Calculate the product inside the logarithm: multiply 387 by 23 to get the new argument for the logarithm.
4. Evaluate the logarithm of the product. Depending on the base of the logarithm (commonly base 10 if not specified), use a calculator or logarithm table to find the value of \(\log (387 \times 23)\).
5. If required, round the result to four decimal places to provide the approximation.

Key Concepts

Properties of Logarithms

Logarithms have specific properties that simplify calculations, such as the product rule: log(a) + log(b) = log(ab). This allows combining sums of logarithms into a single logarithm of the product, making it easier to evaluate or approximate.

Evaluating Logarithms

Evaluating logarithms involves finding the exponent to which the base must be raised to produce a given number. When the base is not specified, it is often assumed to be 10 (common logarithm). Calculators or tables can be used to find decimal approximations.

Decimal Approximation and Rounding

After calculating logarithmic values, results are often approximated to a certain number of decimal places for clarity and precision. Rounding to four decimal places means keeping four digits after the decimal point, adjusting the last digit based on the next digit's value.