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e^(5-4x)=3

e5−4x=3 e^{5-4 x}=3

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Full solution

Q. e5−4x=3 e^{5-4 x}=3
  1. Take Natural Logarithm: First, we need to take the natural logarithm (ln) of both sides to get rid of the exponent.\newlineSo, ln⁡(e5−4x)=ln⁡(3)\ln(e^{5-4x}) = \ln(3).
  2. Simplify Left Side: Using the property of logarithms that ln⁡(ey)=y\ln(e^y) = y, we simplify the left side to get 5−4x=ln⁡(3)5 - 4x = \ln(3).
  3. Move Constant Term: Now, we need to solve for xx. Let's move the 55 to the other side by subtracting 55 from both sides.\newlineSo, −4x=ln⁡(3)−5-4x = \ln(3) - 5.
  4. Isolate xx: To isolate xx, we divide both sides by −4-4.x=ln⁡(3)−5−4x = \frac{\ln(3) - 5}{-4}.

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