perplexus.info :: Just Math : Log of Log equation

Log of Log equation (Posted on 2025-02-22)

Find the unique positive integer 𝑥 > 1 satisfying

log₂log₅x + log₅log₂x = log₂(10/log₂5)

No Solution Yet Submitted by Danish Ahmed Khan

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solution

| Comment 1 of 2

clearvars

rhs=log2(10/log2(5))

for x=2:50

l5=log(x)/log(5);

l52=log2(l5);

l2=log2(x);

l25=log(l2)/log(5);

lhs=l52+l25;

fprintf('%4.2f %10.8f %10.8f %10.8f \n',[x lhs rhs lhs-rhs])

end

find the LHS = RHS at x = 32.

Posted by Charlie on 2025-02-22 12:03:31

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