If I have an equation of the form $Y=A+x^B+C^x$ is it possible to solve for $x$, where $A$, $B$, and $C$ are all rational numbers?
More specifically, is it possible to solve $y=12 + 2x + x^{1.92} + 2^{0.425(x-12)}$ and, if so, how would I do it?
Answer
There is no nice formula that expresses $x$ as a function of $y$. For any particular numerical value of $y$ you can use software to find a value of $x$. For examples, if you ask Wolfram alpha to find $x$ when $y=100$
solve 12+2x+x^1.92+2^(0.425(x−12))=100
you find out that $y$ is
9.0984743836320913466
Since your function is increasing, it would be straightforward to write a python program (or a program in any other language) to find values by bisection, or to build a table of values as in a comment. You could even build a table of values in a spreadsheet.
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