Logarithms

Remember the following.

log a + log b = log ab

log a – log b = log a/b

log aⁿ = n log a

log _n 1 = 0

log _n m = log m / log n

log _n m is undefined if m ≤ 0 or n ≤ 0

Answer : A

Note that p = log 2 and q = log 3

log 1/6 = log 1 - log 6 = 0 - log 6 = -log 2 - log 3 = -p - q

Answer : A

log ₁₀ b = 1 + (1/2)log ₁₀ a = log ₁₀ 10 + log ₁₀ (a^1/2) = log ₁₀ (10a^1/2)

Therefore, b = 10a^1/2.

Answer : E

log x² – (log x)² = 0

2log x – (log x)² = 0

log x(2 – log x) = 0

log x = 0 or log x = 2

x = 1 or 100