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Solve the exponential equation by expressing each side as a power of the same base and then equating the exponents. \( 2^{3 x-4}=4 \) The solution set is \( \{\square\} \)

Ask by Williams Lowe. in Saudi Arabia
Mar 09,2025

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The solution is \( x = 2 \).

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To solve the equation \( 2^{3x-4} = 4 \), we first express 4 as a power of 2. Since \( 4 = 2^2 \), we can rewrite the equation as: \[ 2^{3x-4} = 2^2 \] Now that both sides are powers of the same base (which is 2), we can equate the exponents: \[ 3x - 4 = 2 \] Solving for \( x \), we first add 4 to both sides: \[ 3x = 6 \] Now, divide both sides by 3: \[ x = 2 \] The solution set is \( \{2\} \).

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