IB Maths AI 1.8 Definitions

This page contains our IB Maths AI definitions for 1.8. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Advanced exponents & logs'.

All Topic 1 Sub-topics 1.1: Scientific Notation 1.2: Arithmetic Sequences 1.3: Geometric Sequences 1.4: Interest 1.5: Introduction To Exponents & Logs 1.6: Handling Numbers 1.7: Use Of Technology (HL)1.8: Advanced exponents & logs (HL)1.9: Introduction to complex numbers (HL)1.10: Advanced complex numbers (HL)1.11: Introduction to matrices (HL)1.12: Advanced matrices

base

The initial value of

n

for which a claim is first verified in an induction argument, commonly

n=1

change

A method for rewriting a logarithm in a different base using

\log_ax=\frac{\log_bx}{\log_ba}

, often with

b=10

b=e

common

Describes a logarithm with base

10

, written as

\log x

exponent

A number or expression written as a superscript that tells how many times the base is multiplied by itself, for example

3^4=3\times3\times3\times3

integer

A whole number that can be positive, negative, or zero.

inverse

Describes an operation that undoes another operation; for example, if

a^x=b

then applying

\log_a

b

returns

x

laws

Rules that allow expressions to be rewritten in an equivalent form, for example to simplify or solve equations while keeping the same value.

logarithm

The inverse of an exponential: if

a^x=b

, then

\log_ab=x

, meaning it gives the power needed on base

a

to produce

b

natural

Describes a logarithm with base

e

, written as

\ln x=\log_ex

quotient

A result of division; in a logarithmic identity this refers to combining a fraction inside a single log, such as

\log_a\left(\frac{x}{y}\right)=\log_ax-\log_ay

for suitable positive

x

and

y

rational

Expressible as a ratio of integers, written as $n=\frac{p}{q}$ with integers $p,q$ and $q\neq0$ , allowing the series form of $(1+x)^n$ to be used.

reciprocal

The multiplicative inverse of a non-zero number, so multiplying a value by its reciprocal gives

1

(for example, the reciprocal of

a

\frac{1}{a}

technology

Digital tools such as a graphic display calculator (GDC) or a spreadsheet used to carry out calculations, solve equations, and model financial situations efficiently.

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