Find each value. If applicable, give an approximation to four decimal places. ln 27 + ln 943

Verified step by step guidance

1. Recall the logarithm property that states the sum of logarithms with the same base can be combined as the logarithm of the product: \(\ln a + \ln b = \ln(ab)\).
2. Apply this property to the given expression: \(\ln 27 + \ln 943 = \ln(27 \times 943)\).
3. Calculate the product inside the logarithm: multiply 27 by 943 to get the value inside the logarithm.
4. Evaluate the natural logarithm of the product: find \(\ln(27 \times 943)\) using a calculator or logarithm table.
5. If needed, approximate the value to four decimal places by rounding the result from the previous step.

Key Concepts

Properties of Logarithms

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

Natural Logarithm (ln)

The natural logarithm, denoted ln, is the logarithm with base e (approximately 2.718). It answers the question: to what power must e be raised to get a given number? Understanding ln is essential for evaluating and approximating logarithmic expressions.

Decimal Approximation of Logarithms

When exact values are difficult to find, logarithms can be approximated using calculators. Approximations are often rounded to a specified number of decimal places, such as four, to provide a practical and precise numerical answer.