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2) \( 3^{5-2 x}=1 \)

Ask by Welch Burgess. in Uzbekistan
Dec 22,2024

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\( x = \frac{5}{2} \)

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Mind Expander

To solve the equation \( 3^{5-2x} = 1 \), we can utilize the fact that any non-zero number raised to the power of zero equals one. This means that we can set the exponent equal to zero: \[ 5 - 2x = 0 \] Solving for \( x \): \[ 2x = 5 \] \[ x = \frac{5}{2} \] So, the solution is \( x = 2.5 \). In case you were wondering, any time you have an exponential equation set equal to 1, checking the base's exponent gives a quick path to the solution. Keep in mind that if you're dealing with a different base, the principle remains the same—just solve for the exponent equaling zero!

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