What is the missing exponent in the following equation?
e^? / e^65 = e^38
In the equation e^? / e^65 = e^38, the missing exponent is 103.
To find the missing exponent in the equation e^? / e^65 = e^38, we can start by applying the rule of exponents which states that when dividing two exponents with the same base, you subtract the exponents.
So, on the left side of the equation, e^? / e^65 can be written as e^(? - 65).
Now, we can rewrite the equation as e^(? - 65) = e^38.
Since the bases on both sides of the equation are the same (e), we can conclude that the exponents must also be equal. So, ? - 65 = 38.
To find the value of the missing exponent, we can solve for ?:
? - 65 = 38
Adding 65 to both sides, we get:
? = 38 + 65
Simplifying the right side, we find:
? = 103
Therefore, the missing exponent in the equation e^? / e^65 = e^38 is 103.