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AustraliaVIC
VCE 11 Methods 2023

7.08 Properties of logarithms

Interactive practice questions

Simplify each of the following expressions without using a calculator. Leave answers in exact form.

a

$\log4+\log9$log4+log9

b

$\log_{10}\left(10\right)+\log_{10}\left(10\right)$log10(10)+log10(10)

Easy
1min

Simplify each of the following expressions without using a calculator. Leave answers in exact form.

Easy
2min

Express $\log10x+\log10y$log10x+log10y in simplest form.

Easy
2min

Express $\log\left(\frac{pq}{r}\right)$log(pqr) as the sum and difference of log terms.

Easy
< 1min
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Outcomes

U2.AoS1.17

the key features and properties of the exponential functions, logarithmic functions and their graphs, including any vertical or horizontal asymptotes

U2.AoS1.18

the relationship between an exponential function to a given base and the logarithmic function to the same base as inverse functions

U2.AoS2.1

use of inverse functions and transformations to solve equations of the form Af(nx)+c, and f is sine, cosine, tangent or a^x, using exact or approximate values on a given domain

U2.AoS2.2

exponent laws and logarithm laws, including their application to the solution of simple exponential equations

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