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Is 5^k less than 1,000?
(1) 5^(k-1) > 3000
(2) 5^(k-1) = 5^k - 500
(1) 5^(k-1) > 3000
(2) 5^(k-1) = 5^k - 500
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12 Dec 2003, 16:23
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(1) 5^(k-1) > 3000
(5^k)/(5) > 3000
5^k > 15000
(2) 5^(k-1) = 5^k - 500
5^k/5 - 5^k = -500
5^k (1/5 - 1) = -500
5^k (-4/5) = -500
5^k = -500 * -5/4
5^k = 625
(1) 5^(k-1) > 3000
(5^k)/(5) > 3000
5^k > 15000
(2) 5^(k-1) = 5^k - 500
5^k/5 - 5^k = -500
5^k (1/5 - 1) = -500
5^k (-4/5) = -500
5^k = -500 * -5/4
5^k = 625
