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.

6 mosquitoes

Step-by-step explanation:

64 = 2^x

Use log base 2 both sides

log2(64) = log2(2^x)

log2(2^6) = xlog2(2)

6log2(2) = x

x = 6

Step-by-step explanation:

F(x) = 2^x

64 = 2^x

2^6 = 2^x

x = 6

f(x) = 2^x

log (f(x)) = x log 2

x = log (f(x)) / log 2 = log_2 (f(x))

Therefore, the required logarithmic function is x = log_2 (f(x))

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