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DISCUSS: Comparing Logarithms Which is larger, lo…
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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100 Problem 101 Problem 102 Problem 103 Problem 104 Problem 105

Problem 103 Easy Difficulty

DISCUSS: The Googolplex A googol is $10^{100},$ and a googolplex is $10^{\text { googol }} .$ Find $\log (\log ($ googol $))$ and $\quad \log (\log (\log ($ googolplex $)))$

Answer

$1-\log (\log (g o o g o l))=2$
$2-\log (\log (\log ($googolplex$)))=2$

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Video Transcript

So if we're told that a Google is 10 to the 100 well, we confined the log of log, uh, of 10 to the 100 pretty easily, pretty easily. And and so all we have to do is remember, we have this inside function here, this log rhythm of 10 to the 100. But we can make this 100 into into a coefficient. So this we can convert this to log of 100 times log of 10 friends, log of 10. And so And so now if we plug this into our calculator, this isn't This isn't hard for our calculator to compute. So we have 100 times the log of 10. And so this is simply equal to to this is simply equal to two. So this is our first solution. And then now what we want to do is find We're told that a googol plex is is 10 to the 10 to the 10 to the to the 100. And so remember that 10 to the 100 is a googol plex. So all we have to do now is say we have logged of log, uh, 10 to the 10 to the 100. Also now weaken, Weaken. We write this as log of of 10 to the 100. Because this is our exponents to our 10 of log of long of 10 and so so long based log based 10 here is simply equal to one. Because remember, when we have log of log of X, this is essentially What we're saying we have is we have logged of 10 log base 10 of X. So this is this is what we're saying and so long based 10 of 10 is just one. So this weekend we write this as one. Well, so now we're left with again. Log of 10 to the 100. Well, we have 101 100 times log of 10. It's a long of 10 is again one. This is equal to 100. So this is our solution

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Algebra and Trigonometry

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