How to Learn Exponential and Logarithmic Functions

A structured path through Exponential and Logarithmic Functions — from first principles to confident mastery. Check off each milestone as you go.

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Understand the form f(x) = a * b^x. Identify growth (b > 1) vs decay (0 < b < 1). Graph exponential functions and identify asymptotes.

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Define logarithms as inverses of exponentials. Convert between exponential and logarithmic forms. Evaluate common logs and natural logs.

Master the product rule, quotient rule, power rule, and change of base formula. Simplify and expand logarithmic expressions.

Apply logarithms to solve exponential equations. Apply exponentiation to solve logarithmic equations. Check solutions against domain restrictions.

Explore Euler's number e, the natural exponential function, continuous compounding, and the natural logarithm ln.

Model compound interest, population growth, radioactive decay, pH, and the Richter scale using exponential and logarithmic functions.

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