Question

Sa se calculeze
$log_{ \sqrt{2}-1 } ( \sqrt{3}+1) + log_{ \sqrt{2}+1} ( \sqrt{3}+1)$

Answer 1

log₍√₂₋ ₁₎ (√3 +1) + log₍√₂ ₋₁₎ (√3 +1) ·log₍√₂₊₁₎(√2 -1) =
=log₍√₂₋₁₎(√3+1) ·[1+ log₍√₂₊₁₎(√2 -1)] =
log₍√₂₋₁₎(√3+1)  ·[ log₍√₂₊₁₎(√2+1) + log₍√₂₊₁₎(√2 -1) ]=
= log₍√₂₋₁₎(√3+1) ·log₍√₂₊₁₎[(√2+1)(√2-1)] = log₍√₂₋₁₎(√3+1) · 0 = 0