Applications of indices and logarithms include solving exponential/logarithmic equations and real-world problems. Solving a^x = b: Take log of both sides: x log(a) = log(b), so x = log(b)/log(a). Example: 2^x = 8 → x log(2) = log(8) → x = log(8)/log(2) = 3. Compound interest: A = P(1+r)^n. Growth/decay: N = N₀ × a^t. Taking log simplifies: log(N) = log(N₀) + t log(a). Solving approach: (1) Set up equation; (2) Apply logs to both sides; (3) Use log laws to simplify; (4) Solve for variable. Exam tip: Logarithms convert exponential problems to linear ones. Practice: Half-life problems use N = N₀ × (1/2)^(t/T₁/₂).