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What you should be able to do
- Apply the laws of indices to simplify expressions
- Convert between index and logarithmic form
- Use logarithm laws to evaluate expressions
Study notes
The laws of indices let you combine powers of the same base: multiply by adding indices (a^m x a^n = a^(m+n)), divide by subtracting (a^m / a^n = a^(m-n)), and raise a power to a power by multiplying ((a^m)^n = a^(mn)). Any non-zero base to the power 0 equals 1, and a negative index means a reciprocal (a^-n = 1/a^n). Logarithms are the inverse of indices: if a^x = b then log base a of b = x. The log laws mirror the index laws exactly — log(mn)=log m+log n, log(m/n)=log m−log n, and log(m^k)=k log m.
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Source: JAMB UTME Mathematics syllabus. Type: official. Last checked: 2026-09-17. Practice questions are original Belmadeng material.