Problem 66 - Introductory and Intermediate Algebra for College Students 4th

Question

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{0.3} 19$$

Step-by-Step Solution

Answer

To round to four decimal places, the result should be -1.4624.

Step 1: Use change of base formula

Firstly, apply the change of base formula which states that \( \log_{b}a = \dfrac{\log a}{\log b} \). In this problem, the base (b) is 0.3 and the number (a) is 19. Therefore, we substitute these values into the equation, we get: \( \log_{0.3}19 = \dfrac{\log 19}{\log 0.3} \)

Step 2: Calculate using a calculator

Next, use a calculator to evaluate the right side of the equation. Be sure to remember that the calculator uses base 10 by default, so there is no need for any adjustment when inputing in the values.

Step 3: Round off to four decimal places

Finally, round off the final value obtained to four decimal places. This is a standard practice in many scientific and engineering disciplines to ensure the precision and accuracy of the result.