SOLVING AN EXPONENTIAL EQUATION

SOLVING AN EXPONENTIAL EQUATIONS 
      
  Hello my freinds. Wellcome back to our new class. Today we are going to learn how to solve an exponential equation in two variable. We have diffrent method of solving an exponential equations, the method is determined defending on the nature of the given equation.
    

 EXAMPLE : 
       If six power x plus six power y is the same as fourty two and x plus y is the same as 3, then find the value of x and y?

Image 1 

SOLUTION:
      
  In this given question we have been given two equations with two unknown, so we can solve them simulteneously using subtitution method.
        Firstly we can let the first equation to be equal to equation one, and the second equation to be equal to equation two. However,we used equation two to find equation three by making y to be the subject of the formula from it.

Image 2 

      Hence, we can subtitute equation 3 in equation 1 to change the equation to have only one variable:

Image 3 
        

           Then we let six power x to be equal to  k, so that we will replace it with k and change the format of our equation.

Image 4.

Now everything turned to quadratic equation, so we will solve it using any method of solving quadratic equation to find the value of k.

Image 5


     NOTE: If the product of any numbers is zero, is either one of them must be equal to zero or both of them must be equal to zero.

Now from the above equation, is either k minus thirty six to be equal to zero or k minus six to be equal to zero. Therefore, we can let each one of them to be equal to zero.

Image  6


Now, we found the value of k but remember we said let k be equal to six power x. So we can now replace k with six power x and find the two possible values of x.

Image 7

Now we have the value of x as 2 and 1. Then we use equation three above to find the value of y.



Image 8

Finally we have the values of x and y.


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Comments

Abdullahi Ibrahim kano said…
This was so nice, thank you very much sir.
September 2, 2022 at 4:14 AM
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