Solving the Logarithmic Equation 5*ln(x) = 10

We know x = ln(e^x) for all x in the real numbers then we substitute the expression for x above into the equation (in the Q) and obtain. ln(x) + ln(e^x) = 1 (from substitution from definition above) Equivalently. ln(xe^x) = 1 (log rules)

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x=e^2 Base-e cancels out with the natural log (ln) function, so we can apply it to both sides. We get e^(lnx)=e^2 cancel(e)^(cancel(ln)x)=e^2 Notice base-e and ln cancel, and we're left with x=e^2 as our final answer. Hope this

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