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I would like to know the complete expansion of log(a + b).
For example
log(a * b) = log(a) + log(b); log(a / b) = log(a) - log(b); Similar to this, is there any expansion for log(a + b)?
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To expand logarithms, write them as a sum or difference of logarithms where the power rule is applied if necessary. Often, using the rules in the order quotient rule, product rule, and then power rule will be helpful. To simplify logarithms, write them as a single logarithm.
Adding log A and log B results in the logarithm of the product of A and B, that is log AB. For example, we can write. log10 5 + log10 4 = log10(5 × 4) = log10 20. The same base, in this case 10, is used throughout the calculation.
In general, one doesn't expand out log(a + b); you just deal with it as is. That said, there are occasionally circumstances where it makes sense to use the following identity:
log(a + b) = log(a * (1 + b/a)) = log a + log(1 + b/a) (In fact, this identity is often used when implementing log in math libraries).
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