Use the fact that log2 x = 1 loge 2 loge x and loge x = ln x, for all positive numbers
Chapter 11, Problem 44(choose chapter or problem)
Use the fact that \(\log _{2} x=\left(\frac{1}{\log _{e} 2}\right) \log _{e} x\) and \(\log _{e} x=\) ln x, for all positive numbers x, and part (c) of Example 11.4.7 to show that
\(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n} \quad \text { is } \quad \Theta\left(\log _{2} n\right)\)
Text Transcription:
log _2 x=(frac 1 log _e 2) log _e x
log _e x=
1+frac 1 2+frac 1 3+dots+frac 1 n is Theta(log _2 n)
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