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inna [77]
3 years ago
13

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

Mathematics
1 answer:
-BARSIC- [3]3 years ago
5 0

Answer:

x = 5, y = 5

Step-by-step explanation:

{5}^{x - 3}  \times  {3}^{2y - 8}  = 225 \\ {5}^{x - 3}  \times  {3}^{2y - 8}  = 25 \times 9 \\  {5}^{x - 3}  \times  {3}^{2y - 8}  =  {5}^{2} \times  {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 \\ \huge \red{ \boxed{ x = 5}} \\  \\ {3}^{2y - 8}  = {3}^{2} \\ 2y - 8 = 2(Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal)  \\ 2y = 2 + 8 \\ 2y = 10 \\ y =  \frac{10}{2}  \\ \huge \purple{ \boxed{y = 5}}

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