Find the value of x. log4 65,536 = x

a. x = 32,768
b. x=8
c. x = 65,536
d. x=4

Log4 65,536 = X.

4^x = 65,536, x*Log 4 = Log 65,536, X = Log 65536/Log 4 = 8.

To find the value of x in the expression log4 65,536 = x, we need to understand the logarithmic function and how it works.

The logarithm of a number to a given base is the exponent to which the base must be raised to obtain that number. In this case, we have the logarithm of 65,536 to the base 4, which means we need to find the exponent to which 4 must be raised to equal 65,536.

To solve this, we can rewrite the equation as an exponential equation: 4^x = 65,536.

Now, let's determine the value of x. We can use trial and error or simplifying methods.

By simplifying, we find that 65,536 can be expressed as 4^8. Therefore, x = 8.

So, the correct answer is b. x = 8.