If 10^0.3010 = 2, then find the value of log 29
2025
If 10^0.3010 = 2, then find the value of log 29
- A.
0.698
- B.
2.709
- C.
2.697
- D.
1.696
Attempted by 57 students.
Show answer & explanation
Correct answer: B
Key idea: use the change-of-base formula to convert to common (base 10) logarithms.
Given: log10 2 = 0.3010.
Compute log10 9 = log10 (3^2) = 2 · log10 3 ≈ 2 · 0.4771 = 0.9542.
Now apply change of base: log base 2 of 9 = (log10 9) / (log10 2) = 0.9542 / 0.3010 ≈ 3.170.
Therefore log base 2 of 9 ≈ 3.170. None of the provided options equal this value; the listed answer 2.709 is not correct.