Juan Leonard

Juan Leonard

Answered

2022-10-21

Logarithms equation with tricky transformations
8 x 2 × 5 x + 2 = 1
This one according to wolfram alpha it has nice solution
x = 2 ( log ( 8 ) log ( 5 ) ) log ( 8 ) + log ( 5 )
I see one could guess this solution and just assume left side is increasing function and be done, but I want to see some transformations which could bring me to this solution and I'm stuck.

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Answer & Explanation

giosgi5

giosgi5

Expert

2022-10-22Added 15 answers

8 x 2 × 5 x + 2 = 8 2 5 2 8 x 5 x = 5 2 8 2 40 x .
That is equal to 1 precisely if
40 x = 64 25
and that holds only if
x = log 40 64 25 .

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