Write the logarithmic expression log, as sum or difference of logarithms. Select one: O None of them O log,(8) – log, y O log, y- log, 8- log, x O log, 8 – log, r+ log, y O log, 8 + log,-log, y

A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from each class to be on a school board, how many different board can be selected? Show all work.   Show all work

Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T: R³-R², T(e₁) = (1,3), T(e₂) = (2, -11), and T(e3)= (-3,8), where e₁,e₂, e3 are the columns of the 3x3 identity matrix. a. Is the linear transformation one-to-one? A. T is not one-to-one because the standard matrix A has a free variable. B. T is one-to-one because the column vectors are not scalar multiples of each other. O C. T is not one-to-one because the columns of the standard matrix A are linearly independent. O D. T is one-to-one because T(x) = 0 has only the trivial solution. b. Is the linear transformation onto? O A. T is not onto because the standard matrix A contains a row of zeros. O B. T is onto because the standard matrix A does not have a pivot position for every row. O C. T is not onto because the columns of the standard matrix A span R². O D. T is onto because the columns of the standard matrix A span R².

Rewrite each expression as a single logarithm. Then evaluate the resulting logarithm without using a calculator. 13. log, 405-log, 5 15. log, 1.5 + log,18 17. 2log 124 + 3log 123 + 2log 122