If log₁₀ 2 = 0.3010, find log₁₀ 8.

**The reasoning** The key principle here is the **power rule of logarithms**: log(aⁿ) = n·log(a) Notice that 8 = 2³ (2 × 2 × 2 = 8) So: log₁₀ 8 = log₁₀(2³) Using the power rule: log₁₀(2³) = 3 × log₁₀ 2 Since log₁₀ 2 = 0.3010: log₁₀ 8 = 3 × 0.3010 = **0.9030** **Why the wrong options tempt you** - **Option A (0.6020)**: You multiplied by 2 instead of 3, possibly thinking 8 = 2². Remember: 2² = 4, not 8! - **Option C (0.7525)**: This looks like you tried averaging or did 2.5 × 0.3010. There's no mathematical basis for this. - **Option D (2.4080)**: You multiplied by 8 instead of recognizing that 8 is a power of 2. Don't confuse the number itself with its relationship to the base. **Quick takeaway** When finding log of a number, **always express it as a power of something you already know** — then multiply the log by that power. 8 = 2³, so log 8 = 3 × log 2. Simple!