What is the value of \(x\) in the logarithmic equation \(\log_2 (x) = 3\)?

To find the value of (x) in the equation (\log_2 (x) = 3), we can rewrite the logarithmic equation in its exponential form. The equation states that (x) is the number that we get when we raise the base (which is 2) to the exponent (which is 3).

Therefore, we can express this as:

[

x = 2^3

]

Calculating (2^3) gives us:

[

x = 8

]

This means the correct value for (x) is indeed 8. The logarithm function here indicates that when the base 2 is raised to the power of 3, the result is 8. This understanding of the relationship between logarithms and exponents is fundamental to solving such equations.