Exploring Exponential Equation Puzzle

00:00 7 marks

Consider the following exponential equation puzzle:

Solve \(2^{x+1} \cdot 4^{x-2} = 8^{2x}\).

This problem is divided into two parts:

Part a

3 minutes 3 marks

Question

Express all terms as powers of 2 and simplify the expression \(2^{x+1} \cdot 4^{x-2}\).

Hint Hint

Hint

Remember that \(4 = 2^2\). Substitute and combine the exponents appropriately.

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Complete Answer

\(2^{3x-3}\)

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Part b

5 minutes 4 marks

Question

Using your result from part (a), solve the equation \(2^{3x-3} = 8^{2x}\) for \(x\).

Hint Hint

Hint

Write \(8\) as a power of \(2\) and then equate the exponents.

Answer Answer
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Complete Answer

\(x = -1\)

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