Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to…

Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to a fixed base, find log 10.5 to the same base without using tables.

Correct Answer: Option B

Explanation

log 10.5 = log (frac{21}{2})
= log 21 – log 2
= log(3 x 7) – log 2
= log 3 + log 7 – log 2
= 1.10 + 1.90 – 0.69
= 3 – 0.69
= 2.31