Question

Find the values of x and y if 5 ˣ⁻³ x 3²ʸ⁻⁸ =225

Answer 1

x = 5, y = 5

Explanation:

`{5}^(x - 3) * {3}^(2y - 8) = 225 \\ {5}^(x - 3) * {3}^(2y - 8) = 25 * 9 \\ {5}^(x - 3) * {3}^(2y - 8) = {5}^(2) * {3}^(2) \\ equating \: like \: power \: terms \: from \: both \:\\ sides \\ {5}^(x - 3) = {5}^(2) \\ x - 3 = 2 (Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ x = 3 + 2</p><p> \\ \huge \red{ \boxed{ x = 5}} \\ \\ </p><p></p><p>{3}^(2y - 8) = {3}^(2) \\ 2y - 8 = 2(Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ 2y = 2 + 8 \\ 2y = 10 \\ y = (10)/(2) \\ \huge \purple{ \boxed{y = 5}}`