Why cant algebra calculators without graphing involved solve this equation $2^x=3x-1$

calculator

I know you can plug in 1 and get the answer, but im curious as to why some websites with algebra calculators cannot solve the equation unless the website has some sort of graphic calculator also assigned to the problem?

Best Answer

Polynomials and exponentials do not play nicely together, so a routine algebraic solution will not work. People are good at finding clever solutions, but calculators are not. People are biased toward toward integer solutions, so can see that $1$ is a solution (somewhat) easily. Calculators do not have the same bias, so $1$ is no different from $0.998$ to them.

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