Rationalize the denominator of fraction with numerator square root of negative 36 and denominator the quantity of 2 minus 3i plus the quantity 3 plus 2i Options: fraction with numerator 6 plus 30i and denominator 24
fraction with numerator negative 6 plus 30i and denominator 26
fraction with numerator 6 plus 30i and denominator 26
fraction with numerator 6 plus 30i and denominator 24 minus 10i

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."