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.