Solve the logarithm for x without using a calculator?

Rewrite both sides in terms of the same base, namely, 2. 2^(2(x² + 1)) = 2^(5(-x)) 2x² + 2 = -5x 2x² + 5x + 2 = 0 (2x + 1)(x + 2) = 0 x = - 1/2 or x = -2.

2^(2x^2 + 2) = 2^(-5x) 2x^2 + 2 = -5x 2x^2 + 5x + 2 = 0 2x^2 + 4x + x + 2 = 0 (2x + 1)(x + 2) = 0 x = -1/2 , -2.

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