In the logarithmic expression . . . log(base 4) 8 , how does the base 4 become base 2?

Here is how it is suppose to be worked out:

log(base2)8 / log(base2)4 =>
log(base2)2^3 / log(base2)2^2 => 3/2

To understand how the base 4 can become base 2, we need to use the change of base formula for logarithms.

The change of base formula states that if you have a logarithm with base b, you can convert it to a logarithm with base a by taking the logarithm of the number you're trying to evaluate and dividing it by the logarithm of the new base.

In this case, we have log(base 4) 8 and want to convert it to base 2. Using the change of base formula, we can write:

log(base 4) 8 = log(base 2) 8 / log(base 2) 4

Now, let's simplify this expression step by step:

First, let's evaluate log(base 2) 8. This is asking the question, "What power of 2 equals 8?" The answer is 3, because 2^3 = 8.

Next, let's evaluate log(base 2) 4. This is asking the question, "What power of 2 equals 4?" The answer is 2, because 2^2 = 4.

Now we can substitute these values back into the original expression:

log(base 4) 8 = 3 / 2

So, log(base 4) 8 is equal to 3/2 when expressed in base 2.