PLZ HELP, IT'S ALGEBRA 2: 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.

Question

Astrid1 · Answer

Okay to start this  off we can do :
$$f(x)=2^x$$
We're going to turn f(x) into y
$$y=2^x$$
Switch X and Y and take log of both sides.
$$\log(x)=\log(2^y)$$
Appy the rule of log and then divide both sides by 2
$$y=\log(x)/\log(2)$$
Apply change of base rule
$$y=\log_2(x)$$
Now we convert it to 64°
$$y=\log_2(64)$$
64 as 2^6
$$y=6\log_2(2)$$
Evaluate the log_2(2) and we should get y=6.
Our logarithmic function is $$y=\log_2(x)$$ and the answer is when it is 64° is y=6.

NicktheBlade16 · Answer

Alright, thank you man, i appriacte it alot

Astrid1 · Answer

I hope I helped!!

Axolotlqueen · Answer

my head hurts now