Given log₁₀2 = 0.3010, find log₂10 (correct to 4 decimal places).

Concept / Approach

• Use the change-of-base formula: log ⁡ 𝑏 𝑎 = log ⁡ 10 𝑎 log ⁡ 10 𝑏 log b ​ a= log 10 ​ b log 10 ​ a ​
• Here, log ⁡ 2 10 = log ⁡ 10 10 log ⁡ 10 2 log 2 ​ 10= log 10 ​ 2 log 10 ​ 10 ​ .

Step-by-step calculation log ⁡ 10 10 = 1 log 10 ​ 10=1 log ⁡ 2 10 = 1 0.3010 = 3.322259... log 2 ​ 10= 0.3010 1 ​ =3.322259...Rounded to 4 d.p. ⇒ 3.3223

Common pitfalls

• Inverting the fraction incorrectly (using 0.3010 0.3010 instead of its reciprocal).
• Forgetting that log ⁡ 10 10 = 1 log 10 ​ 10=1.

Final Answer3.3223