(In reply to
Puzzle Answer by K Sengupta)
Dividing both sides by 9^x, we have:
1 +(4/3)^x =(16/9)^x
Then, substituting n= (4/3)^x, we must have:
1+n=n^2 => n^2 - n -1 = 0
=> n = (1+/-V5)/2
If n=(1-V5)/2, then n must be < 0 as V5>1
In that situation, (4/3)^x will give us:
x*log(4/3) as a non-real quantity. Contradiction.
Accordingly, we must have n ={(1+V5)/2}
Then, x*log(4/3) = log{(1+V5)/2 }
=> x ~= (0.8089876402)/(0.1249387366)
~= 1.67272
Edited on May 29, 2022, 11:01 pm
Explanation to Puzzle Answer
