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Chapter 1: Problem 60

Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places. $$\log _{3} 30$$

Short Answer

Expert verified
Answer: The value of $$\log _{3} 30$$ rounded to four decimal places is approximately 3.0940.

Step by step solution

01

Apply the change of base formula

To convert the logarithm in base 3 to a natural logarithm, we will apply the change of base formula. We have: $$\log_b a = \frac{\ln a}{\ln b}$$ For $$\log _{3} 30$$, we plug in the values of $$a$$ and $$b$$ into the formula: $$\log _{3} 30 = \frac{\ln 30}{\ln 3}$$
02

Calculate the value of the natural logarithm

Now that we have converted the logarithm to a natural logarithm, we can use a calculator to find its value rounded to four decimal places. $$\log _{3} 30 = \frac{\ln 30}{\ln 3} \approx 3.0940$$ So, $$\log _{3} 30 \approx 3.0940$$.

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