log-15-5-2-log-15-3-log-15-75-

Question Number 181154 by mathlove last updated on 22/Nov/22

{({l o g}_{15} 5)}^{2} + ({l o g}_{15} 3) ({l o g}_{15} 75) = ?

Answered by SEKRET last updated on 22/Nov/22

\log_{15} (3) = a \log_{15}^{} (5) = 1 - a

\log_{15} (15 \cdot 5) = 1 + \log_{15} (5) = 2 - a

{(1 - a)}^{2} + a \cdot (2 - a) = a^{2} - 2 a + 1 + 2 a - a^{2} = 1

answer 1

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Commented by mathlove last updated on 22/Nov/22

t h a n k s