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Solve e^x = 7

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Answer
ln⁡(7)≈1.946\boxed{\ln(7) \approx 1.946}

Substituting x=ln⁡(7)x = \ln(7) back into the original equation gives eln⁡(7)=7e^{\ln(7)} = 7, which confirms the solution is correct.

Problem: Solve for xx in the equation ex=7e^x = 7.

Steps

  1. Take the natural logarithm of both sides
    ln⁡(ex)=ln⁡(7)\ln(e^x) = \ln(7)
  2. Apply the logarithm power rule
    xln⁡(e)=ln⁡(7)x \ln(e) = \ln(7)
  3. Simplify using ln⁡(e)=1\ln(e) = 1
    x=ln⁡(7)x = \ln(7)

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