To simplify the expression log4 log2, we start by recognizing that the logarithm can be represented in terms of a common base. Using the change of base formula, we can express log4 in terms of base 2:
log4 = log2(4)- Since
4 = 22, we havelog2(4) = log2(22) = 2.
Now we replace log4 in our original expression:
log4 log2 = 2 log2
Thus, the expression simplifies to 2 log2. This means that the logarithm of 4, when multiplied by the logarithm of 2, equals twice the logarithm of 2 itself.