(IGCSE & GCSE) Additional Math Indices & Logarithms

Explore indices and logarithms through a GCSE-aligned crash course for high school learners. Practice-driven instruction guides you from a solved example to similar problems with pause-and-solve steps and flexible pacing.

Master negative powers and index rules by rewriting 3^(4−x) and 9^(x+1) in terms of y, with y = 3^x, yielding 81/y and 9y^2.

Explore how indices and surds rationalize denominators by multiplying with conjugates, convert to rational numbers, and simplify expressions like eight divided by three minus square root of five.

Rationalize a denominator with square roots by multiplying to flip the sign, cancel radicals, and simplify to -1 minus the square root of six.

Practice five indices and logarithms questions, reinforcing exponent rules, zero exponents, fractional powers, and expressing results in terms of y, for IGCSE and GCSE math.

Practice question 6 demonstrates simplifying products of square roots, factoring radicals, applying exponents, and expanding and simplifying squared binomials with surds for clear, quick math mastery.

Practice question 7 demonstrates rationalizing denominators using conjugate surds, solving two examples with square roots, and simplifying to results like 3√2−3 and 17−12√2.

Solve exponential equations by equating exponents when bases match, and handle special bases like 1, -1, or 0; apply with examples such as 4^x = 1/16.

Solve exponential simultaneous equations by equalizing bases and rewriting as linear relations, then apply elimination to find x and y, yielding x=1 and y=2.

Explore logarithms by converting between exponential and logarithmic forms, identify the base, exponent, and result, and practice with examples like 4^2=16 and 10^3=1000.

Distinguish common logarithms (base ten, lg) from natural logarithms (base e, ln) and learn to write, simplify, and solve log equations with a scientific calculator.

Practice solving logarithmic equations by taking logs to isolate x, using common or natural logarithms, and calculators. Work through four questions and pause to attempt them yourself.

Explore the four laws of logarithms: change of base, product, quotient, and power. See how to apply them with examples like solving equations using the same base.

Explore laws of logarithms through practice questions, applying power and quotient rules and working with logs of numbers and bases to solve for unknown logs.

Celebrate completing this engaging GCSE additional math course and explore more topics, while sharing a review and posting questions in the Q&A for quick help.