Find the value of p if 5 ^p-3 ×3 ^2p-8 =225
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Answered by
3
5^(p - 3) x 3^(2p - 8) = 225
(5^p x 5^-3) x (3^2p x 3^-8) = 225
(5^p x 5^-3) x (9^p x 3^-8) = 225
(5^p x 9^p) x (5^-3 x 3^-8) = 225
(5^p x 9^p) = 225 x (5^3 x 3^8)
(45)^p = (3^2 x 5^2) x (5^3 x 3^8)
(45)^p = (3^10 x 5^5)
45^p = (3^2)^5 x 5^5
45^p = 9^5 x 5^5
45^p = 45^5
Therefore p = 5 ——> Answer
(5^p x 5^-3) x (3^2p x 3^-8) = 225
(5^p x 5^-3) x (9^p x 3^-8) = 225
(5^p x 9^p) x (5^-3 x 3^-8) = 225
(5^p x 9^p) = 225 x (5^3 x 3^8)
(45)^p = (3^2 x 5^2) x (5^3 x 3^8)
(45)^p = (3^10 x 5^5)
45^p = (3^2)^5 x 5^5
45^p = 9^5 x 5^5
45^p = 45^5
Therefore p = 5 ——> Answer
Answered by
0
Answer:
p=6
Step-by-step explanation:
5^6-3×3^2×6-8=225
3125-2900=225
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