It’s easier for us to evaluate logs of base 10 or base e, because calculators usually have log and ln buttons for these. When the base is anything other than 10 or e, we can use the change of base formula.
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The general log rule relates the logarithmic function to an exponential function. It tells us that log_a(y)=x and a^x=y are equivalent, and similarly, that log_a(x}=y and a^y=x are equivalent.
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Remember that an exponent tells us how many times to multiply the base by itself. Logarithms tell us how many times we multiply one number by itself in order to get a different number. Exponentials and logarithms are related to one another with the general log rule.
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When there’s no base on the log, it means we’re dealing with the common logarithm, which always has a base of 10. Any logarithm with base e is a natural logarithm, and we write the log with ln instead of log.
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Laws of logarithms (or laws of logs) include product, quotient, and power rules for logarithms, as well as the general rule for logs (and the change of base formula we’ll cover in the next lesson), can all be used together, in any combination, in order to solve log problems.
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You can always evaluate logs using the general log rule, but sometimes, depending on the value of the base and the argument, simplifying the exponential expression can be a little tricky.
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