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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.

Sagot :

Marcodbbsaidn

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.

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