Logarithmic and Exponential Functions in MYP Year 5 Extended Maths

Q: What does this topic include?

Exponential functions of the form a*b^x and their inverses, logarithms. Covers the three core log laws (product, quotient, power), change of base, and solving equations such as 2^x = 20 by taking logs of both sides. Applications include compound growth, decay, and population models. Sitting at the end of Unit 1 Extended, it pulls together fractional exponents and index laws, giving you the algebraic toolkit to handle non-linear growth questions in Criterion A and D tasks.

Q: Key tip for solving exponential equations?

When bases cannot be matched (e.g. 5^x = 17), don't guess. Take log of both sides: x*log5 = log17, then x = log17/log5. Use any base consistently. A frequent slip: log17/log5 is NOT log(17/5) â€” log17 - log5 equals log(17/5), not the quotient of logs. Check by substituting back. For 3^(2x+1) = 81, prefer matching bases (81 = 3^4) and equate indices, since it's faster and exact.

Explore logarithms and exponential functions in MYP Year 5 Extended Maths. Includes log laws, exponential growth and decay, and solving exponential equations.

Practice

Logarithmic & Exponential Functions

180 min100 marks

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A New Kind of Function

Exponential and logarithmic functions represent a significant expansion of the function families students have encountered so far. Rather than repeated addition (linear) or repeated multiplication of a variable (polynomial), exponential functions model situations where the rate of change is proportional to the current value — a pattern that appears throughout science, finance, and the natural world.

Exponential Functions

An exponential function has the form f(x) = a · b^x, where b > 0 and b ≠ 1. When b > 1, the function models growth; when 0 < b < 1, it models decay. Students explore the key features: y-intercept, asymptotic behaviour as x → −∞, and the role of the base b in controlling the rate.

Real-World Applications

Population growth and bacterial reproduction
Radioactive decay and half-life problems
Compound interest: A = P(1 + r/n)^nt

Logarithms as Inverses

The logarithm is defined as the inverse of the exponential function. If a^y = x, then log_a(x) = y. Students must be comfortable moving fluently between exponential and logarithmic form.

Logarithm Laws

The three key laws mirror the index laws:

log(AB) = log A + log B
log(A/B) = log A − log B
log(Aⁿ) = n log A

These laws allow students to expand, condense, and simplify logarithmic expressions — a skill that underpins solving exponential equations.

Solving Exponential Equations

When the variable is in the exponent and the bases cannot be matched, logarithms provide the solution method: take logs of both sides and apply the power law. For example, solving 3^x = 20 gives x = log 20 / log 3.

Assessment Relevance

This topic is most commonly tested under Criterion A (multi-step solving) and Criterion D (modelling with exponential functions in context). Students who grasp logarithms here will find the DP transition significantly smoother.

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