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.

The required logarithmic function is

and x=6

Step-by-step explanation:

Given : 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 , where x is the number of mosquitoes.

To find : How he can convert this equation to a logarithmic function when the temperature is 64 degrees?

Solution :

We have given the exponential function,

Converting into logarithmic function,

Taking log both side

by logarithmic property

Now, we have given f(x)=64

We can verify it by,

On caparison the base,

Therefore, The required logarithmic function is

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3