I need help finding the inverse of this formula
So basically I’m trying find the inverse to this formula and I’m having trouble getting it could anyone help me out I would appreciate it thank you
$$f_{3t}(x) = \frac{\log(25-(-1.8(x)))}{\log(x)}$$
edit: to clarify I am under the assumption that the inverse currently does not exist as I was trying to make a formula to solve this polynomial (x^n-1.8x=25) once I had that solved I could change up the numbers to eventually find a formula for (x^n+ax) I had worked on this for about 3 weeks and while I did manage to obtain the inverse to n I need the inverse of that equation to solve for it hence the original question I have only lightly skimmed through your answers but I will go back and check some of the links you provided me hopefully together we can find the inverse formula for this equation I also didn’t mention that it was currently unsolved as 1 I didn’t know if that’s true and 2 I didn’t want to discourage anyone from trying hopefully that answers the reason behind the question if you have anything else you want me to explain like the work I did to get that formula or other feel free to let me know! P.S sorry for the lack of punctuation I’m just a bit excited I can finally have others to have a look at it.
edit#2: here is what the inverse should look like image of the inverse and here was the closest I got to finding itmy attempts to approximate the inverse hope all of this helps!
edit#3: here is all the work I’ve done to get the formula sorry in advance for all the disorganization
there’s more but those are either not important or completely failed as stated before hope this helps!
$\endgroup$ 131 Answer
$\begingroup$According to this answer, there is no definite inverse. Are you asking for an approximation? What is the specific question of the, say, homework, or did you think of this question up? You might helpful sources under inverse if you search log. Usually writing "basically" as the reason of why you want to solve a problem isn't enough or even useful. (Also note that I am not smart enough to come up with an approximation, as I am only a seventh-grader).
$\endgroup$ 2Your function $f$ is an open bijection, $f^{-1}$ exists, but does not have an easy analytical expression.
