Topics
4. Logarithmic and exponential functions
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AustraliaVIC
VCE 12 Methods 2023

4.09 The natural logarithm

Lesson
Worksheet
Practice

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

Find the value of $5\log_ee$5loge​e.

Easy
< 1min

Simplify $e^{\ln w}$elnw.

Easy
< 1min

Consider the value of $\log_e2$loge​2

Easy
< 1min
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Outcomes

U34.AoS1.2

graphs of the following functions: power functions, y=x^n; exponential functions, y=a^x, in particular y = e^x ; logarithmic functions, y = log_e(x) and y=log_10(x) ; and circular functions, 𝑦 = sin(𝑥) , 𝑦 = cos (𝑥) and 𝑦 = tan(𝑥) and their key features

U34.AoS1.7

the key features and properties of a function or relation and its graph and of families of functions and relations and their graphs

U34.AoS1.18

sketch by hand graphs of polynomial functions up to degree 4; simple power functions, y=x^n where n in N, y=a^x, (using key points (-1, 1/a), (0,1), and (1,a); log x base e; log x base 10; and simple transformations of these

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