Logarithmic Function and Root
Logarithmic functions and roots are mathematical concepts that are often used in various fields of study, including mathematics, science, and engineering.

Logarithmic Function
The logarithmic function is the inverse of the exponential function. It is denoted by "log" and is used to find the exponent to which a specific base must be raised to obtain a given number. In this case, we are looking for the logarithm of 1728 with a base of 2.

Root
The root of a number is the inverse operation of raising a number to a power. In this case, we are looking for the square root of 3.

Calculating the Logarithm and Root
To calculate the logarithm of 1728 with a base of 2 and a root of 3, we can use the properties of logarithms and roots. First, we can express 1728 as 2^6, as 2^6 = 64, 64^3 = 1728. So, log base 2 of 1728 can be written as log base 2 of (2^6) = 6.
Then, we can find the square root of 3, which is approximately equal to 1.732.

Final Calculation
Log base 2 of 1728 root 3 = 6 * 1.732 = 10.392
Therefore, log base 2 of 1728 root 3 is equal to approximately 10.392.