To solve the equation \( 3 - 5^{3x} = 18 \), follow these steps:
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Isolate the exponential term: \[ -5^{3x} = 18 - 3 \] \[ -5^{3x} = 15 \]
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Multiply both sides by \(-1\): \[ 5^{3x} = -15 \]
At this point, we notice that the left-hand side (\(5^{3x}\)) is always positive for real values of \(x\), while the right-hand side (\(-15\)) is negative. Since a positive number cannot equal a negative number, there are no real solutions for the equation.
Therefore, the solution is that there are no real solutions for the equation \( 3 - 5^{3x} = 18 \).
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