Problem 110 - College Algebra

Question

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

Step-by-Step Solution

Answer

To find \(\log _{14} 283\), use the change of base formula. Thus, \(\log _{14} 283 = \frac{\log 283}{\log 14}\). Use your calculator to find the values of \(\log 283\) and \(\log 14\), and divide the first result by the second one.

Step 1: Understand the problem

To find \(\log _{14} 283\), we need to know what power we have to raise 14 to get 283. However, our calculator only provides log base 10 or natural log (base e). The problem thus lies in translating our base-14 logarithm into a form which the calculator can comprehend.

Step 2: Use the change of base formula

The change of base formula is \(\log_b a = \frac{\log_d a}{\log_d b}\). We can use this to translate \(\log _{14} 283\) into \(\frac{\log 283}{\log 14}\). This is now an equation that your calculator can understand.

Step 3: Use your calculator

Now that we have \(\frac{\log 283}{\log 14}\), we can use your calculator to work this out. First, calculate \(\log 283\), then calculate \(\log 14\), and finally divide the first result with the second one.