SL 1.1—Using standard form

SL 1.2—Arithmetic sequences and series

SL 1.3—Geometric sequences and series

SL 1.4—Financial apps – compound interest, annual depreciation

SL 1.5—Intro to logs

SL 1.6—Simple proof

SL 1.7—Laws of exponents and logs

SL 1.8—Sum of infinite geo sequence

SL 1.9—Binomial theorem where n is an integer

AHL 1.10—Perms and combs, binomial with negative and fractional indices

AHL 1.11—Partial fractions

AHL 1.12—Complex numbers – Cartesian form and Argand diag

AHL 1.13—Polar and Euler form

AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers

AHL 1.15—Proof by induction, contradiction, counterexamples

AHL 1.16—Solution of systems of linear equations

IB Mathematics Analysis and Approaches SL 1.5—intro to Logs Notes

Logarithms: An Introduction

Logarithms are the inverse of exponentiation when solving for the exponent, while radicals can be used to solve for the base when the exponent is fixed.

Let's say we have $a$, $b$, and $c$ such that $a^b = c$.

To rearrange this equation for $a$, we can use a radical, making $a = \sqrt[b]{c}$.

But if we want to rearrange for $b$ instead, we have to use a logarithm.

This equation looks like: $$b = \log_a c$$

So essentially, if you have $\log_a c$, it's asking "What number do I have to raise $a$ to in order to make $c$?"

Example

If $2^3 = 8$, then $\log_2 8 = 3$. If $10^x = 1000$, then $\log_{10} 1000 = x$, which we know is 3.

Base 10 Logarithms

The base 10 logarithm, often written as $\log_{10}$ or simply $\log$, is the most commonly used logarithm in everyday applications.

It represents the power to which 10 must be raised to obtain a given number.

Example

$\log_{10} 100 = 2$ because $10^2 = 100$
$\log_{10} 1000 = 3$ because $10^3 = 1000$

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IB Mathematics Analysis and Approaches SL 1.5—intro to Logs Notes

Logarithms: An Introduction

Base 10 Logarithms

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Logarithms: An Introduction

Base 10 Logarithms

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Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics

IB Mathematics Analysis and Approaches SL 1.5—intro to Logs Notes

Logarithms: An Introduction

Base 10 Logarithms

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Logarithms: An Introduction

Base 10 Logarithms

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Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics