Everything Power Zero Is One, Right?
True or false :
lo g x 1 = 0 for every x > 0 .
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3 solutions
I konw x=1 is not in Domain of log! But 1°=1 . May you explain more?
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The matter is that using 1 0 = 1 is the same that 1 4 = 1 , that is the reason why lo g 1 1 = 0 , because by that logic lo g 1 1 = 4 is true too and it means lo g 1 1 = lo g 1 1 ⇒ 0 = 4 , which is false...... I hope this explains what you want to know, feel free of asking whatever you want
True! That got me!
The name of the problem gives away the answer though.
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I left this problem as level 2 at the beginning, the idea with a name which make the answer sort of obvious is confusing, there are a lot of ones which think that is impossible to make a problem with the answer in the name, also, in brilliant all we are supposed to be here for making and solving problems, it has no sense to be guessing only because the name says something, and I guess that @Pi Han Goh , thinks similar about his problem
As far as I know, logarithm of base 1 is not defined (indeterminate), so I am afraid your explanation cannot convince me.
but by definition of log, logarithm to the base 1 is never defined,there is a restriction that the base can never be equal to 1....
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That's just why the statement is false, 1 > 0 and we can't take x = 1 ....
logarithmic functions are defined only when x > 0 and x not equal to 1.
Sorry I don't understand, I always thought that 1 0 = 1 , is this wrong? Why?
We know that 1 n = 1 is true for all n (except for ∞ ). Let me take two examples: 1 0 = 1 and 1 1 = 1 . But, lo g 1 1 = 0 and lo g 1 1 = 1 .
Suppose lo g 1 1 = 0 and lo g 1 1 = 1 are true, then
lo g 1 1 = lo g 1 1 ⇒ 0 = 1 .
There is a contradiction. Therefore, lo g 1 1 is undefined. We can then conclude that lo g x 1 is true when x = 1 .
This is false for x = 1 .
The matter is that using 1 0 = 1 is the same that 1 4 = 1 , that is the reason why lo g 1 1 = 0 , because by that logic lo g 1 1 = 4 is true too and it means lo g 1 1 = lo g 1 1 ⇒ 0 = 4 , which is false...... I hope this explains what you want to know, feel free of asking whatever you want