This very simple equation 7^x = 6^x +2 provides an approximate solution of 1.2808
when using graphs.
The caret sign "^" represents exponentiation.
I could easily also represent this problem as 4^x=3^x+7 where x is 2 - but how do you calculate x?
I cannot find the solution to this problem using logarithms.
I must be missing something very simple here - could some genius please enlighten me.
Thank you for your responses.
I am afraid that my level of mathematical knowledge does not extend to closed form solutions.
Are you saying that this equation cannot be solved without using graphs or trial and error ?
Is the mathematics for closed form solutions too advanced to be shown in a few lines ?
Well, there is/are solutions to the problem. Closed form means an explicit answer that involves a finite combination of elementary functions. For example, when you find the roots of a quadratic, you will get the answers in the form of square roots and fractions. However, there doesn't seem to be such a solution for the equations you have provided.
In this case we have to resort to non-closed form solutions in the form of either an inexact answer, an infinite sum or the use of special non-elementary functions.