An algebra problem by sina aghrel

Algebra Level 2

Solve log ⁡ 5 [ log ⁡ 5 ( log ⁡ 5 x ) ] = 0 \log _{ 5 }{ [\log _{ 5 }{ (\log _{ 5 }{ x)]=0 } } }


The answer is 3125.

Sina Aghrel by sina aghrel , 22, Australia

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1 solution

Sophie Crane
Sep 6, 2014

l o g 5 [ l o g 5 ( l o g 5 x ) ] = 0 log_5 [log_5 (log_5 x)] = 0

l o g 5 ( l o g 5 x ) = 1 log_5 (log_5 x) = 1

l o g 5 x = 5 log_5 x = 5

x = 5 5 = 3125 x = 5^5 = 3125

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