Question

360 can be written as 2^x * 3^y * 5, where x and y are positive integers.

Work out the value of x and the value of y.

Answer 1

x = 3, y = 2

Explanation:

`360 = {2}^(x) * {3}^(y) * 5 \\ \\ (360)/(5) ={2}^(x) * {3}^(y) \\ \\ 72 = {2}^(x) * {3}^(y) \\ \\ 8* 9 = {2}^(x) * {3}^(y) \\ \\ {2}^(3) * {3}^(2) = {2}^(x) * {3}^(y) \\ \\ equating \: like \: terms \: on \: both \: sides \\ {2}^(3) = {2}^(x) \\ \\ \implies \: x = 3 \\ \\ {3}^(2) = {3}^(y) \\ \\ \implies \: y= 2 \\ \\`