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Problem 450

AMC 12 late, AIME early

Algebra Difficulty 4.8 Find the answer

4. Solve the equation $\left(\log _{4}(x+1)+\sqrt{\log _{4}^{2}(x+1)+1}\right)\left(\log _{4}(3 x+5)+\sqrt{\log _{4}^{2}(3 x+5)+1}\right)=1$ .

Your answer

Official solution

Answer: $x=-\frac{2}{3}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.