solve for x without using softwares log_(sqrt(x))2+log_6x^x=4
metodystap9
Open question
2022-08-19
solve for without using softwares Is there any nice way to solve this equation without wolfram?
Thanks.
Answer & Explanation
Adelyn Mercado
Beginner2022-08-20Added 13 answers
Rewriting
leads to the equation
which cannot be solved analytically ( or cannot be solved either). Plotting the function shows two roots, the first close to , the second close to . For the solution, Newton is the simplest root-finder. Strating from a "reasonable" guess , it will update it according to
For the first root, using , the successive iterates are , which is the solution for six significant figures. Limiting to a single iteration, we should have obtained
For the second root, using , the successive iterates are , which is the solution for six significant figures. Limiting to a single iteration, we should have obtained
As you can see, all of this could be done using a pocket calculator.
Taliyah Reyes
Beginner2022-08-21Added 6 answers
I am pretty sure the isn't solvable with Algebra II, unless you resort to the mess that is complex logs. However:
which is a quadratic in except for the pesky x coefficient. Using the quadratic formula anyway, and evaluating the logs,
This is definitely solvable. However, The only way I can come up with a numerical solution is graphing the two sides.