Exponential functions and logarithms (other)

Exponential functions and logarithms can be explored beyond the basic forms $a^x$ and $\log_a x$. This includes understanding their behavior for different bases, transformations, and how they interact in equations and inequalities.

Important properties

• Exponential functions grow or decay rapidly depending on the base.

• Changing the base of an exponential or logarithm changes its rate of growth or decay.

• Logarithms are the inverses of exponential functions.

• Exponential and logarithmic equations can often be solved by rewriting one side to match the other or by using properties of exponents and logarithms.

• Transformations (shifts, stretches, reflections) apply to exponential and logarithmic graphs similarly to other functions.