how do u find the inverse of
2^-t/4
so far i know that you change the x andy
so that gives u y=2^-t/4
x=2^-x/4
then log of 2 is the base , but what do u do with the exponent
for the expression
y =2 ^ (-t/4), the inverse function is the function which t = f(y). If we solve the above function for t in terms of y:
taking the log of both sides
log(y) = log(2 ^ (-t/4))
log(y) = (-t/4)*log(2)
(log(y))/(log(2))=-t/4
-4*(log(y))/(log(2))=t
To find the inverse of the function 2^(-t/4), you need to solve for t in terms of the function's output.
Step 1: Start with the function
2^(-t/4)
Step 2: Replace the function with y
y = 2^(-t/4)
Step 3: Swap the variables t and y
t = 2^(-y/4)
Step 4: Solve for y
To solve for y, you will need to isolate the exponential term. Begin by taking the logarithm of both sides of the equation. Since the base of the exponential function is 2, we will take the logarithm base 2.
log2(t) = log2(2^(-y/4))
Step 5: Apply the rules of logarithms
Using the rule that log_a(b^c) = c * log_a(b), the equation becomes:
log2(t) = (-y/4) * log2(2)
log2(t) = (-y/4) * 1
log2(t) = -y/4
Step 6: Isolate y
Multiply both sides of the equation by -4 to isolate y:
-4 * log2(t) = y
Finally, you have found the inverse of 2^(-t/4), which is given by:
y = -4 * log2(t)