2

How can I convert the image below into TeX?

Logarithm Problem

  • 2
    Can you show us what you've tried? – Werner Oct 5 '18 at 22:21
  • Haven't tried anything... the change of base is something which I haven't learned how to do. – Punala Kiripitige Oct 5 '18 at 22:22
  • Do you want to solve the problem or print it? – egreg Oct 5 '18 at 22:23
  • I want to print it. – Punala Kiripitige Oct 5 '18 at 22:23
  • How about \log_{2}? – aloneprism Oct 5 '18 at 22:27
11

This is simple: the logarithmic function is \log, so you want something like

\documentclass{article}
\usepackage{amsmath}

\begin{document}

Find $n$ given that
\[
\log_{2} 3 \, \log_{3} 4 \, \log_{4} 5 \, \dotsm \, \log_{n} (n+1)=10
\]

\end{document}

enter image description here

By the way, this is a case where amsmath needs a little help, so \dotsm should be used to denote “dots for multiplication”. Also I added thin spaces to reduce the clutter.

The answer is, of course, 1023.

If you fear that the above can be ambiguous, then use \cdot (and \dotso in order not to have a series of five centered dots):

\documentclass{article}
\usepackage{amsmath}

\begin{document}

Find $n$ given that
\[
\log_{2} 3 \cdot \log_{3} 4 \cdot \log_{4} 5 \cdot \dotso \cdot \log_{n}(n+1)=10
\]

\end{document}

enter image description here

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