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nathanshields eNotes educator| Certified Educator

`log 0 = x` can be rewritten as `10^x = 0`.  Since no value of x solves this equation, the expression log(0) is undefined.

However, notice that `10^x` gets pretty close to zero if you use large negative values for x.  In fact, you can get `10^x` to be as close to zero as you desire if you choose a low enough x value.  For this reason we can say `lim_(x->0+) log x = -infty`

adrienne77 | Student

Logorithims can be expressed as exponents and vice versa. For example, a^b = c can be expressed as loga (c)=b so, 3^2=9 or log3 (9) = 2... Following this logic would lead us to, in the case of base 0, logb(0) =a or b^a=0. This equation has no solution since there is no number that can be raised to any power and equal 0 so therefore, it is undefined. Hope this helps :)

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