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 defined as the inverse of an exponential function.
When you raise a number with an exponent, there comes a result.
Let's say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
The data are represented by the exponential function
f(x) = 2ˣ
To convert this equation to a logarithmic function when the temperature is 64 degrees.
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
x = 6
The logarithmic function when the temperature is 64 degrees is given as ln f(x) = x ln 2.
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