Solving Exponential Equations Calculator

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 Solving exponential equation calculator is a tool used to solve the exponential equations.  In exponential

equations variables appear exponent like y = b^y here b is a positive real number and y may be negative or

positive, e^x + 2, a^x = b^y, these are some examples of exponential equations. Radioactive decay, population

growth and some increasing decreasing functions are solved by using exponential functions. 



Example 1: - Solve given exponential equation 2^ (5x – 1) = 32

Solution: - Some of the steps involved are as follow:-


Step 1: Given exponential equation is

                2^ (5x – 1) = 32

Step 2: We know 32 = 2 * 2 * 2 * 2 * 2 = 2^5

Now we can write as

               2^ (5x -1) = 2^5

Step 3: Now we have same base is both side so we equate exponent in both side ad get

             5x -1 = 5

             Let we add 1 in both side and get

            5x = 5 + 1

            5X = 6

           Divide both sides by 5 and get    
  
           x = 5/6  
                
           So, the solution is 5/6



Example 2: Solve given exponential equation (1/3) ^ (3x – 2) = 1/81


 Solution: - Some of the steps involved are as follow:-


 Step 1: Given exponential equation is   
     
              (1/3) ^ (3x – 2) = 1/81

Step 2: We can write 81 = 3 * 3 * 3 * 3 = 3^4
      
             Now we can write 

 (1/3)^ (3x – 2) = (1/3) ^4

Step 3: We have same base is both side so we compare exponent in both side and get

3x – 2 = 4

We add both sides

3x = 4+2

3x = 6

Divide both sides by 3 and get

x = 2 
                
  So, the solution is 2.



 

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