1. Show that

    $\displaystyle \frac{d}{dx}\log_b(x) = \frac{1}{x\ln(b)}

    where $ \log_b(x)$ denotes the logarithm to the base $ b$ of $ x$.

  2. Work out the definition of logarithms using a complex base $ b$.

  3. Try synthesizing a sawtooth waveform which increases by 1/2 dB a few times per second, and again using 1/4 dB increments. See if you agree that quarter-dB increments are ``smooth'' enough for you.

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