Mathematics (AS)·Logarithmic and exponential functions · NSSCAS 2.2.1
Logarithms & their laws
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In this lesson you will discover that a logarithm is just the answer to one question: what power? You will learn to swap between index form and log form both ways, and to evaluate simple logs in your head. You will prove and use the three laws of logarithms to combine and expand expressions. Finally you will solve a log equation and safely reject any invalid answer.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.2.1):
- Interpret the relationship between logarithms and indices, converting aˣ = b into x = log_a b and back again.
- Use the laws of logarithms — log(xy) = log x + log y, log(x/y) = log x − log y, log(xⁿ) = n log x — together with the special values log_a a = 1 and log_a 1 = 0.
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