If log520 = x, find x

Analyze the question: "log520 = x" most likely means log base 5 of 20, i.e. log₅20 = x. The options (all around 1.3 to 2.5) fit this reading. Log base 10 of 520 would be about 2.716, which isn't an option.

Concept: Change of base formula: log₅20 = log₁₀20 / log₁₀5

Solution:

• log₁₀20 = log₁₀2 + log₁₀10 = 0.3010 + 1 = 1.3010
• log₁₀5 = 0.6990

x = 1.3010 / 0.6990 ≈ 1.861

Check: 5^1.861 = 5^(1 + 0.861). 5^0.861 = e^(0.861 × 1.6094) = e^1.3857 ≈ 4.0, so 5^1.861 ≈ 20. ✓

Alternative method: log₅20 = log₅(4 × 5) = 1 + log₅4 = 1 + (0.6020/0.6990) = 1 + 0.861 = 1.861.

Answer: C. 1.861.

Tip: For "log base a of b" questions, split b into factors that include the base (here 20 = 4 × 5), so you get 1 + log₅4. Memorize log 2 = 0.3010 and log 5 = 0.6990 (they add up to 1), since they come up often in JAMB.