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Super Exponentiation Surmise IV (Posted on 2023-10-23) Difficulty: 3 of 5
Find all possible values real number x of that satisfy this equation:

      42x = 2-x

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Alternate method Comment 2 of 2 |

4^(2^x) = 2^(-x)
(2^x)*ln4 = -x*ln2
2^(x+1)*ln2 = -x*ln2
2^(x+1) = -x
(x+1)*ln2 = ln(-x), which if there is to be a defined solution leads to
rhs
à x<0,  LHS à x >= -1<p><p>

By inspection, x=-1 is the only solution

Edited on October 24, 2023, 5:05 pm
  Posted by Kenny M on 2023-10-24 17:04:30

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