Question

Daniel is looking over some data regarding the temperatures of countries and how the temperature relates to the number of mosquitoes. The data are represented by the exponential function f(x) = 2x, where x is the number of mosquitoes. Explain how he can convert this equation to a logarithmic function when the temperature is 64 degrees.

Answer 1

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.