Wood Pena
01/23/2023 · Senior High School
Solve the equation. \( e^{5 x-1}=\left(e^{4}\right)^{-x} \)
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Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( e^{5x-1}=(e^4)^{-x} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(e^{5x-1}=\left(e^{4}\right)^{-x}\)
- step1: Multiply the exponents:
\(e^{5x-1}=e^{4\left(-x\right)}\)
- step2: Set the exponents equal:
\(5x-1=4\left(-x\right)\)
- step3: Multiply the numbers:
\(5x-1=-4x\)
- step4: Move the variable to the left side:
\(5x-1+4x=0\)
- step5: Add the terms:
\(9x-1=0\)
- step6: Move the constant to the right side:
\(9x=0+1\)
- step7: Remove 0:
\(9x=1\)
- step8: Divide both sides:
\(\frac{9x}{9}=\frac{1}{9}\)
- step9: Divide the numbers:
\(x=\frac{1}{9}\)
The solution to the equation \( e^{5x-1}=\left(e^{4}\right)^{-x} \) is \( x=\frac{1}{9} \) or \( x=0.\dot{1} \).
Quick Answer
\( x=\frac{1}{9} \) or \( x=0.\dot{1} \)
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