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Base e

Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 25 of 46.

One base shows up so often that it has its own letter: e, a fixed number about 2.718. Like π its decimals never end, and like π it is a constant, not an unknown. It appears whenever something grows continuously, every instant instead of once a year.

The log base e has its own name too: the natural log, written ln. Like any log it undoes its own power: ln⁡(ex)=x\ln\left({e}^{x}\right) = x. To solve ex=6{e}^{x} = 6, take ln of both sides: x=ln⁡(6)x = \ln\left(6\right), about 1.79. Keep the answer in its exact form; a calculator's ln key gives the decimal when you need one.

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Challenge

Solve ex=9{e}^{x} = 9. Write the exact answer as a line of its own, x = ..., using ln.

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ex=9e^{x} = 9

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