Pure Mathematics 3: Logarithmic and Exponential Functions

Flashcards covering the properties of logarithms, exponential functions, and linearization techniques from Pure Mathematics 3.

Relationship between logarithms and indices

A core understanding in mathematics used to manipulate and solve equations by applying the laws of logarithms, excluding the change of base.

$e^x$ and $\ln(x)$

Inverse functions characterized by specific definitions and properties, including distinct graphical representations.

$$y = e^{kx}$$

Exponential graphs that are studied for both positive and negative values of $k$.

Equations and inequalities with unknowns in indices

Mathematical problems such as $2^x < 5$, $3 \times 2^{3x-1} < 5$, or $3^{x+1} = 4^{2x-1}$ that are solved using logarithms.

Linear form of $y = kx^n$

A relationship transformed by logarithms into $\ln(y) = \ln(k) + n \ln(x)$, which is linear in $\ln(x)$ and $\ln(y)$.

Linear form of $y = k(a^x)$

A relationship transformed by logarithms into $\ln(y) = \ln(k) + x \ln(a)$, which is linear in $x$ and $\ln(y)$.

Gradient and intercept

Values used after transforming a relationship to linear form to determine unknown constants.