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

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Question 185729This question is from textbook Alegbra 2
: Explain why the expression log+%283%2C+-1%29 and log+%281%2C+1%29 are not defined. This question is from textbook Alegbra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log+%283%2C+%28-1%29%29 Start with the given expression


y=log+%283%2C+%28-1%29%29 Set "y" equal to the expression


3%5Ey=-1 Use the property to rewrite the equation.



Now the question is: what value of "y" will make 3%5Ey equal to -1? Since there is NO value of "y" that will make 3%5Ey negative (because 3%5Ey is ALWAYS positive), this means that there are no solutions to 3%5Ey=-1


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


So that's why log+%283%2C+%28-1%29%29 is undefined


In fact, log+%28b%2C+%28x%29%29 is undefined where b%3E1 and x%3C=0


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log+%281%2C+%281%29%29 Start with the given expression


log+%2810%2C+%281%29%29%2Flog+%2810%2C+%281%29%29 Use the change of base formula log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29 to rewrite the expression.


0%2F0 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 log+%281%2C+%281%29%29 is undefined.