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%I #12 Jun 28 2023 08:22:00
%S 7,2,7,1,6,0,1,5,1,4,1,2,4,2,5,9,2,4,3,0,4,4,7,0,8,4,4,0,0,9,5,2,1,7,
%T 6,9,3,5,4,5,8,9,0,4,5,5,6,4,5,8,3,3,0,4,1,4,2,5,7,7,7,6,4,1,7,5,2,9,
%U 0,8,6,8,4,3,2,3,0,5,7,7,3,3,5,5,0
%N Decimal expansion of x = 0.7271601514124259243... solution to 1 + 3^x = 5^x.
%e 0.7271601514124259243044708440095217693545890455645833041425777641752908684323...
%t RealDigits[x /. FindRoot[1 + 3^x == 5^x, {x, 1}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Jun 28 2023 *)
%o (PARI) print(c=solve(x=0,1, 1+3^x-5^x)); digits(c\.1^default(realprecision))[^-1] \\ [^-1] to discard possibly incorrect last digit. Use e.g. \p999 to get more digits. - _M. F. Hasler_, Oct 31 2019
%Y Cf. A329334 (continued fraction).
%Y Cf. A242208 (1 + 2^x = 4^x), A328900 (2^x + 3^x = 4^x), A328905 (1 + 2^x = 5^x).
%K nonn,cons
%O 0,1
%A _M. F. Hasler_, Oct 31 2019
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