Answer:
the answer if you are trying to find it in log form will be y=log_2(x) and the answer for when the value is 64 is y = 6.
Step-by-step explanation:
To make this into a logarithmic function we must understand that logarithmic functions are the inverses of exponential functions.
knowing this we can start by doing f(x) = 2^x.
We first will makes f(x) = to y so we get y=2^x.
Next we switch the x and y and take the logarithm of both sides. This will get us log(x) = log(2^y).
apply the rule of logarithms and then divide both sides by log 2 so that then we end up with y=log(x)/log(2).
Then apply the change of base rule so that it now looks like y=log_2(x).
This is our logarithmic function. But we must convert it to when the temperature is 64 degrees.
This will give us y=log_2(64).
We then will express our 64 as 2^6.
finally we can make our equation y= 6log_2(2).
We can evaluate the log_2(2) and we get our answer of y=6.
This gives us our logarithmic function which is y=log_2(x) and our answer for when it is 64 degrees which is y=6.
