Given log₁₀2 = 0.3010, evaluate log₁₀80.

Concept / Approach

• Factorize 80 = 8 × 10 = 2 3 × 10 80=8×10=2 3 ×10.
• Use log rules: log ⁡ ( 𝑎 𝑏 ) = log ⁡ 𝑎 + log ⁡ 𝑏 log(ab)=loga+logb, log ⁡ ( 2 3 ) = 3 log ⁡ 2 log(2 3 )=3log2.

Step-by-step calculation log ⁡ 10 80 = log ⁡ 10 ( 2 3 ) + log ⁡ 10 10 = 3 log ⁡ 10 2 + 1 log 10 ​ 80=log 10 ​ (2 3 )+log 10 ​ 10=3log 10 ​ 2+1 = 3 ( 0.3010 ) + 1 = 0.9030 + 1 = < 𝑚 𝑎 𝑟 𝑘 > 1.9030 < / 𝑚 𝑎 𝑟 𝑘 > =3(0.3010)+1=0.9030+1=1.9030

Quick checkSince 80<100, log ⁡ 10 80 log 10 ​ 80 should be just under 2; 1.9030 is reasonable.

Final Answer1.9030