SOLUTION: solve for x in the equation logxbase3 = 3*x-25

Question 274524: solve for x in the equation logxbase3 = 3*x-25
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

I don't think I've ever seen one like this before, but there is a solution as you can see from the graph.

What I did was make y = 3x-25.

since 3x-25 = log(3,x), then I also made another equation of y = log(3,x).

The intersection of those 2 equations is the solution.

That solution is somewhere around x = 9.

The original equation is:

log(3,x) = 3x-25

if x equal 9, then this equation becomes:

log(3,9) = 3*9 - 25 which becomes:

log(3,9) = 27-25 = 2

this is true if and only if 3^2 = 9 which it does, so the solution of x = 9 is good.

I still haven't been able to figure out how to derive it from the formula.

If x had to be an integer, then it would be a relatively simple matter of looking at different values of x until you found a solution.

The formula of log(3,x) = 3x-25 would be a clue that x had to be greater than 8 because the log of a number can't be negative. 3*8 = 24-25 = -1 would have been invalid, so you would have had to start at x = 9. If so, you would have had it on the first go.

If x did not have to be an integer than that method for a solution would have been a lengthy process of interpolation until you narrowed into the actual solution.

Sorry I couldn't do any better. Everything I tried turned into an identity which is not enough to solve the problem.

If you do find a solution algebraically, let me know.

In the meantime, I hope this helped a little.

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