what is the missing exponent in the following equation?
(e^(?)/(e^(65)=e^(38)
The missing exponent in the equation is -27.
The correct equation is:
(e^(65 - ?))/(e^65) = e^38
To solve for the missing exponent, we can apply logarithmic rules. Taking the natural logarithm (ln) of both sides of the equation:
ln((e^(65 - ?))/(e^65)) = ln(e^38)
Using the rule ln(a/b) = ln(a) - ln(b):
ln(e^(65 - ?)) - ln(e^65) = ln(e^38)
Using the rule ln(e^x) = x:
(65 - ?) - 65 = 38
Simplifying:
-? = 38
? = -38
that is wronggg
Apologies for the incorrect response. Let's solve the equation correctly:
(e^(?))/(e^65) = e^38
To simplify the left side of the equation, we can use the quotient rule of exponents:
e^(? - 65) = e^38
Now, since the bases are the same, we can set the exponents equal to each other:
? - 65 = 38
To solve for ?, we can add 65 to both sides:
? = 38 + 65
? = 103
Therefore, the missing exponent in the equation is 103.