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. (please show work)

Answer 1

The logarithmic function when the temperature is 64 degrees is given as
ln f(x) = x ln 2.

What is a logarithmic function?

A logarithmic function is the inverse of an exponential function. It is to be noted that all exponential functions can be written as logarithmic functions.

Hence, to convert the mathematical statement above into a logarithmic function we say:

f(x) = 2ˣ

ln f(x) = ln 2ˣ

ln f(x) = x ln 2

Ln 64 = x Ln 2

Let f(x) = 64;

Hence,

Ln 64 = x ln 2

Divide both sides by  ln 2 to get x

ln 64/ln 2 = x

Hence,

x = ln 64/ln 2

= 6

Learn more about Logarithmic Functions at:
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