Answer:
A, log 64
Step-by-step explanation:
your answer A, log 64 is correct. i will explain why below:
2 log 4, log 2 and log 2 have the same bases (10), meaning they are able to be added easier. but before we add, we use the Power Rule of Logarithms on 2 log 4
the Power Rule says that we can move an exponent in a logarithm to the front then solve. this also applies to the reverse, as we can move 2 back as an exponent of 4 and solve
2 log 4 ---> log 4² < simplify the exponent and we get log 16
we can now use the Product Rule of Logarithms where log x + log y = log(xy)
we can use that on the first two terms of the addition
log 16 + log 2 ----> log (16 × 2) = log 32
now we can apply the other log 2 to the rule but instead with log 32
log 32 + log 2 ---> log (32 × 2) = log 64
our answer is log 64
