4. Logarithmic and exponential functions

4.01 Transformations of exponential functions

INVESTIGATION - The number e

4.02 Transformations of the natural exponent function

4.03 Applications of exponential functions

4.04 Logarithms and indices

4.05 Properties of logarithms

4.06 Equations with logarithms

4.07 Graphs of logarithms

4.08 Transformations of logarithms

4.09 The natural logarithm

VCE 12 Methods 2023

4.03 Applications of exponential functions

Interactive practice questions

Solve $3^x=27$3x=27.

Easy

< 1min

Solve the equation $10^x=0.01$10x=0.01.

Easy

< 1min

Solve $\left(\sqrt{2}\right)^k=0.5$(√2)k=0.5.

Medium

1min

Between which two consecutive integers does the solution of $x$x to the equation $3^x=57$3x=57 lie?

Easy

< 1min

Outcomes

U34.AoS1.6

modelling of practical situations using polynomial, power, circular, exponential and logarithmic functions, simple transformation and combinations of these functions, including simple piecewise (hybrid) functions.

U34.AoS1.13

the features which enable the recognition of general forms of possible models for data presented in graphical or tabular form

U34.AoS2.3

composition of functions, where f composite 𝑔, 𝑓 ∘ 𝑔, is defined by (𝑓 ∘ 𝑔)(𝑥) = 𝑓(g(x)

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