Разберёмся сперва с числителем:
(1-log(5)3)(log²(5)3 +log5(3) +1) =(1-log(5)3)(log(3)5 +log(5)3 +1)
log²(5)3 = log(3) 5
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(1-log(5)3)(log(3)5 +log(5)3 +1) / ( log(3)5 + log(5)3 +1 ) log(5) 5/3 =
= 1-log(5)3 / log(5)5 - log(5)3 = 1-log(5)3 / 1 - log(5)3 = 1