Problem 110 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The value of \(\log _{14} 283\) is the result obtained upon executing the operation on the calculator using the Change of Base formula.

Step 1: Identify the variables

In this exercise, the base (b) is 14 and the argument of the logarithm (a) is 283.

Step 2: Apply the Change of Base formula

Since the basic calculator has a standard base of 10 or e, we can use the Change of Base formula which is \(\log_b a = \log_c a / \log_c b\). Here, substitute a with 283 and b with 14 to get \(\log_{14} 283 = \log_c 283 / \log_c 14\). You may use any value for c, but for most calculators, using 10 or e (natural log) is easiest.

Step 3: Enter the values into your calculator

Now, calculate the values using your calculator. Make sure to do 'log(283) divided by log(14)' if using log base 10, or 'ln(283) divided by ln(14)' if using natural log.

Step 4: Compute the solution

After entering the values into your calculator, compute to get the answer.