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Exponentials & Logarithms

Review question

When does $9^x - 3^{x+1} = k$ have one or more real solutions?
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Ref: R7384

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Question

The equation \[9^x - 3^{x+1} = k\] has one or more real solutions precisely when

\(k \geq -9/4\),
\(k > 0\),
\(k \leq -1\),
\(k \geq 5/8\).