Ch. 4 - Inverse, Exponential, and Logarithmic Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 4 - Inverse, Exponential, and Logarithmic Functions

Problem 31

Chapter 5, Problem 31

Use a calculator to find an approximation to four decimal places for each logarithm. ln 144,000

Verified step by step guidance

Recognize that the problem asks for the natural logarithm of 144,000, which is written as $\ln 144,000$.

Recall that the natural logarithm function, $\ln x$, is the logarithm to the base $e$, where $e \approx 2.71828$.

Use the logarithm property to break down the number if needed: $\ln 144,000 = \ln (1.44 \times 10^5) = \ln 1.44 + \ln 10^5$.

Apply the logarithm power rule: $\ln 10^5 = 5 \ln 10$, and remember that $\ln 10$ is a known constant approximately equal to 2.3026.

Use a calculator to find the values of $\ln 1.44$ and $\ln 10$, then add them according to the expression above to get the approximate value of $\ln 144,000$ to four decimal places.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Natural Logarithm (ln)

The natural logarithm, denoted as ln, is the logarithm to the base e, where e is approximately 2.718. It answers the question: to what power must e be raised to get a given number? Understanding ln is essential for interpreting and calculating logarithmic values.

Use of Calculators for Logarithms

Calculators often have a dedicated ln button to compute natural logarithms directly. Knowing how to input values and interpret the output is crucial for finding accurate approximations, especially for large numbers like 144,000.

Rounding to Decimal Places

Rounding involves adjusting a number to a specified number of decimal places for simplicity and clarity. In this problem, the answer must be rounded to four decimal places, which requires understanding rounding rules to ensure precision.

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