Chapter 4: Problem 144
Without using a calculator, find the exact value of \(\log _{4}\left[\log _{3}\left(\log _{2} 8\right)\right]\).
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Chapter 4: Problem 144
Without using a calculator, find the exact value of \(\log _{4}\left[\log _{3}\left(\log _{2} 8\right)\right]\).
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Evaluate each expression without using a calculator. $$ \log _{2}\left(\log _{3} 81\right) $$
Evaluate each expression without using a calculator. $$ \log _{5}\left(\log _{2} 32\right) $$
Students in a psychology class took a final examination. As part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. The average score for the group, \(f(t),\) after \(t\) months was modeled by the function $$ f(t)=88-15 \ln (t+1), \quad 0 \leq t \leq 12 $$ a. What was the average score on the original exam? b. What was the average score after 2 months? 4 months? 6 months? 8 months? 10 months? one year? c. Sketch the graph of \(f\) (either by hand or with a graphing utility). Describe what the graph indicates in terms of the material retained by the students.
Evaluate or simplify each expression without using a calculator. $$ e^{\ln 125} $$
Exercises \(150-152\) will help you prepare for the material covered in the next section. a. Simplify: \(e^{\ln 3}\) b. Use your simplification from part (a) to rewrite \(3^{x}\) in terms of base \(e\)
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