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Chapter 1: Problem 59

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. $$\log _{2} 15$$

Short Answer

Expert verified
Question: Convert the logarithm $\log_2 15$ to a natural logarithm, rounding to four decimal places. Answer: $\log_2 15 \approx 3.9073$

Step by step solution

01

Apply the Change-of-Base Formula

Given the logarithm: $$\log _{2} 15$$ Apply the change-of-base formula: $$\log_b a = \frac{\ln a}{\ln b}$$ In this case, a = 15 and b = 2: $$\log_2 15 = \frac{\ln{15}}{\ln{2}}$$
02

Calculate the Value of the Logarithm

Using a calculator, find the value of the expression: $$\frac{\ln 15}{\ln 2}$$ Make sure to round the result to four decimal places: $$\log_2 15 \approx 3.9073$$

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Most popular questions from this chapter

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