Exponential equations and logarithms
Logarithms for IB Analysis and Approaches HL: definition, laws, change of base and exponential and logarithmic equations, with IB exam questions.
Logarithms are the operation that "undoes" a power: they answer the question "to what exponent must the base be raised to obtain this number?". In this topic you learn to calculate and transform logarithms and to solve equations in which the unknown is in an exponent or inside a logarithm, something that appears every year in Paper 1.
Recommended order
Start with the exponential equations that are solved by equating bases; then study logarithms and their properties, which allow you to solve those that cannot be equated, and finish with logarithmic equations, where you must always check the solutions. At the end you will find IB exam questions grouped by type.
Powers and radicals (topic 1) and quadratic equations.
Sections in this topic
Exponential equations
Solve exponential equations in IB: equating bases, the substitution t = a^x and common factors, with worked examples and common mistakes.
3 worked examples Section 2Logarithms: definition, properties and change of base
Definition of a logarithm, log and ln, product, quotient and power laws, change of base and how to solve a^x = b, for IB Analysis and Approaches HL.
3 worked examples Section 3Logarithmic equations
How to solve logarithmic equations in IB: a single logarithm, substitution, different bases, checking solutions and systems with exponentials.
3 worked examples End of topicIB exam questions: topic 2
IB exam questions on logarithms and exponential and logarithmic equations, by type and level, with worked solutions.
31 exercises · 4 ★★★ levelStuck on this topic?
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