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Find all real solutions of: log base 2 of (25^(x+3) - 1) = 2 + log base 2 of (5^(x+3) + 1).

1. -1
2. 5
3. -2
4. -3

Correct answer: -2

Solution

LHS - RHS form: 25^(x+3) - 1 = 4*(5^(x+3)+1). Let t = 5^(x+3): t² - 4t - 5 = 0, so (t-5)(t+1) = 0. Since t > 0, t = 5, giving 5^(x+3) = 5¹, so x = -2.

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