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

Answer:

$x = 6$

Step-by-step explanation:

Given

$f(x) = 2^x$

$f(x) = 64$ --- The temperature

Required

Solve for x (convert to logarithmic function)

We have:

$f(x) = 2^x$

Substitute: $f(x) = 64$

$2^x = 64$

To convert to logarithmic function, simply take the log of both sides.

i.e.

$\log(2^x) = \log(64)$

Rewrite as:

$x\log(2) = \log(64)$

Make x the subject

$x = \frac{\log(64)}{\log(2)}$

Express 64 as 2^6

$x = \frac{\log(2^6)}{\log(2)}$

Rewrite as:

$x = \frac{6 *\log(2)}{\log(2)}$

$x = 6$