On a log base 10 scale between 20 and 30 what is the approxi

On a log base 10 scale, between 20 and 30, what is the approximate location of 26

I know the answer is 64 % but I just want to know how to get that answer, please show all work !

thank you

Solution

Suppose point c exist between a & b. (b>a)

Location c = { ( log c - log a) / ( log b - log a) } x 100

In our question, a=20 b=30 c=26

Location of 26 = {( log26-log20) / (log30-log20)} x 100

= 64.7 %