Maths: Applications and Interpretation · Number and algebra. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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An exponent (power) tells you how many times a base is multiplied by itself. The laws of exponents let you combine powers of the same base: add the powers when multiplying, subtract when dividing, and multiply them for a power of a power.
A logarithm is the reverse question: what power of the base gives this number? So log10 1000 = 3 because 103 = 1000. The statements ax = b and loga b = x say exactly the same thing.
Your calculator has log (base 10) and ln (base e, where e ≈ 2.718). Use them to solve equations where the unknown is in the power.
In (2x3)4 students raise only the x3 to the power and leave the 2 alone. The power applies to every factor in the bracket: 24 × x12 = 16x12.
Answer: x = 3.29
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