SOLUTION: Explain why the expression {{{log (3, -1)}}} and {{{log (1, 1)}}} are not defined.

Question 185729This question is from textbook Alegbra 2
: Explain why the expression and are not defined. This question is from textbook Alegbra 2

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Set "y" equal to the expression

Use the property

to rewrite the equation.

Now the question is: what value of "y" will make equal to -1? Since there is NO value of "y" that will make negative (because is ALWAYS positive), this means that there are no solutions to

This in turn means that you CANNOT take the log of a negative number (or zero).

So that's why is undefined

In fact, is undefined where and

--------------------------------------

Start with the given expression

Use the change of base formula to rewrite the expression.

Evaluate the log of 1 to get 0.

Now remember, division by zero is undefined. So we cannot go further.

So this shows us that is undefined.
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