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Problem 257

AMC 10/12, early questions

Algebra Difficulty 4.0 Find the answer 7. tekmovanje v znanju matematike za dijake srednjih tehniških in strokovnih šol · Slovenia

Problem:

Reši enačbo $\log_{3}(\log_{2} x + 12) + 2 = 4$ in rešitev zapiši v obliki ulomka.

Your answer

Official solution

Solution:

Enačbo najprej uredimo $\log_{3}(\log_{2} x + 12) = 2$ . Upoštevamo definicijo logaritma in zapišemo $3^{2} = \log_{2} x + 12$ . Enačbo ponovno uredimo in dobimo $\log_{2} x = -3$ . Rešimo $2^{-3} = x$ . Rešitev je $x = \frac{1}{8}$ .

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