How to solve this equation using logs How do solve this equation for x using logarithms? 4^x = 6^x-3 If it is not possible using logarithms, please provide another way. Thank you in advance
Cristofer Watson
Answered question
2022-10-22
How to solve this equation using logs How do solve this equation for x using logarithms?
If it is not possible using logarithms, please provide another way. Thank you in advance
Answer & Explanation
silenthunter440
Beginner2022-10-23Added 19 answers
In the most general case, equations such as do not show explicit solutions and numerical methods (such as Newton) must be used. Considering that we look for the zero of function
starting from a reasonable guess , Newton method will update the guess according to
Let us consider the case of your equation
By inspection, , show that the solution is quite close to ; so, let us use and apply the method. This will generate the following iterates
which is the solution for seven significant figures. However, we can do it faster considering instead
which is much more linear. Doing the same would lead to the following iterates