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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.

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

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