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6.06 The natural logarithm

Interactive practice questions

Which of the following logarithmic functions is known as the natural log?

The logarithmic function with base $\pi$π.

A

The logarithmic function with base $1$1.

B

The logarithmic function with base $\frac{1}{e}$1e.

C

The logarithmic function with base $e$e.

D

The logarithmic function with base $10$10.

E
Easy
< 1min

State the value of $\ln e$lne.

Easy
< 1min

Which of the following are the correct logarithmic forms of the equation $e^x=3$ex=3? Choose all the correct options.

Easy
< 1min

Find the value of $5\log_ee$5logee.

Easy
< 1min
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Outcomes

3.1.1.4

recognise the qualitative features of the graph of 𝑦=log_𝑎(𝑥) (𝑎>1), including asymptotes, and of its translations 𝑦=log_𝑎(𝑥)+𝑏 and 𝑦=log_𝑎(𝑥+𝑐)

3.2.2.1

define the natural logarithm ln 𝑥 = log_e x

3.2.2.2

recognise and use the inverse relationship of the functions 𝑦=𝑒^𝑥 and 𝑦=lnx

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