Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

If $3^{2x}=64$ , what is the value of $3^{-x}$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $3^{2x}=64$ and $3^{2x}=(3^x)^2$ , then $(3^x)^2=64$ and so $3^x=\pm 8$ . Since $3^x>0$ , then $3^x=8$ . Thus, $3^{-x}=\frac{1}{3^x}=\frac{1}{8}$ .

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