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    Different way for logarithms?

    Growing by Pi
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      professionalbronco M0★ M1★ M2★ M3 M5★
      last edited by professionalbronco

      So we need to solve the equation \(\pi^x=10^9.\) In order to solve for \(x\), we just need one simple step: take \(\log_{\pi}\) of both sides. This means that

      $$\log_{\pi}\pi^x=\log_{\pi}10^9\implies x=\log_{\pi}10^9\approx 18.1. $$

      This however, cannot be done with a calculator. (A calculator only has log and log base \(e\).)

      The Daily Challenge with Po-Shen Loh is the best!
      aops user = captainnobody

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