Problem 100 - Introductory and Intermediate Algebra for College Students 4th

Question

Explain how to use your calculator to find \(\log _{14} 283\)

Step-by-Step Solution

Answer

The short answer for \(\log _{14} 283\) using \(\log _{10}\) would be found by performing the following calculation: \(\frac{\log _{10} 283}{\log _{10} 14}\). The numerical answer will depend on the calculator used.

Step 1: Identify the inputs for the change of base formula

Identify the number from which to take the logarithm (\(a\)) and the base of the logarithm (\(b\)). In the provided exercise, \(a = 283\) and \(b = 14\). You will use this for the change of base formula.

Step 2: Apply change of base formula using a available base

Use the base your calculator provides, typically 10 or \(e\), and apply the formula \(\log _{b} a = \frac{\log _{k} a}{\log _{k} b}\). Transform \(\log _{14} 283\) to \(\frac{\log 283}{\log 14}\), using \(\log\) as \(\log _{10}\), which is available on calculators.

Step 3: Compute the result

Compute the result using your calculator by first finding \(\log 283\), then finding \(\log 14\), and finally dividing the first by the second.