Solving log^2(x2)=x explicitly?

jorgejasso85xvx

jorgejasso85xvx

Answered question

2022-11-19

Solving log 2 ( x 2 ) = x explicitly?
I'm having problems getting a proper step-by-step solution to this equation.
log 2 ( x 2 ) = x
I know the results are 2 and 4, but so far I can get only solutions like these:
2 x = x 2 or log ( x ) x = log ( 2 ) 2 .
I'd like something along the lines of x =
Is it possible with some basic knowledge?

Answer & Explanation

martinmommy26nv8

martinmommy26nv8

Beginner2022-11-20Added 16 answers

No. There is in fact a third solution, x 0.77, but you cannot find it using elementary algebraic methods. The best you can do is to "guess" these solutions (by inspection in the case of the positive ones, or by using a numerical method) and then prove using Calculus that there can be no others (by comparing the growth rates of the two functions).

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