Question

log4 128 - log4 8 simplify

Answer 1

Using the property of logarithms, which states that log(a) - log(b) = log(a/b), we can simplify the expression:

log4 128 - log4 8 = log4 (128/8)

Since 128/8 = 16, we have:

log4 (128/8) = log4 16

Now, we need to find the exponent to which 4 should be raised to obtain 16. In other words, we need to find x in the equation 4^x = 16.

By observing that 4^2 = 16, we can conclude that x = 2. Therefore:

log4 16 = 2

So, log4 128 - log4 8 simplifies to 2.