Quick questions on Euler's number e and natural logarithms for HSC Maths Advanced: the definition of e as the base whose curve y=e^x has gradient 1 at (0,1), the natural logarithm ln x as the inverse of e^x, sketching y=e^x and y=ln x as reflections in y=x, transformations of y=e^x, and solving e^x=k and ln x=k in exact and decimal form

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the natural logarithm ln x as the inverse of e^x?

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Just as

\log_2 x

undoes

2^x

, the logarithm to base

e

undoes

e^x

. Logarithms to base

e

are so common they get a special name and symbol: the natural logarithm, written

\ln x

. So

What is transforming the graph of y = e^x?

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The number

e

is just a particular base, so every transformation from the previous page applies to

y = e^x

unchanged; the trick is the same, track the asymptote, the intercept and the range as you move the curve.

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