log-log graphs are not the same as a log graph. A log-log graph is useful for turning monomials into lines, which is exactly what a Bode plot is. But this is a good point. Maybe "exponential function" is the wrong terminology. "Function with an exponent" is more apt.
> stock price charts are sometimes logarithmic.
Stock price charts are logarithmic when the movement of a stock is exponential over the time frame being looked at. Stock prices, in general, are kind of related to perception as well. A $4 stock that moves +/- $2 is perceived very differently than a $100 stock that moves +/- $2. The perception of a price delta is relative to the current price, not the absolute dollar amount of the movement. This is why stock prices exhibit compound returns, which is of course an exponential function.