Thread: Is this very simple equation impossible to solve without graphs or trial and error ?

Hi,

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.

Regards,

Zorrozac

Originally Posted by zorrozac

Hi,

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.

Regards,

Zorrozac

Are you only looking for closed form solutions?

Originally Posted by wonderboy1953

Are you only looking for closed form solutions?

There are no closed form solutions to these equations.

Hi,

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 ?

Regards,

Zorrozac

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.

So the answer to "can this simple equation be solved using logarithms alone?" is NO.

Thanks to all who contributed, especially Vlasev.

Best regards,

Zorrozac