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can we use logarithms to find the number of digits in a to the power B say the number is n lets represent the possible values of n using a scale now we make equal units with multiples of 10 so that we cover a range from 1 to 10,000 so if the number a to the power B is 9 itll lie between 1 and 10 if its 400 it lie between 100 and 1000 now what if we find the log to the base 10 of these numbers the log of 1 is 0 the log of 10 to the base 10 will be 1 what will be the log of 100 to the base 10 it will be the log of 10 squared to the base 10 that will equal 2 times log of 10 to the base 10 which equals 2 and similarly we have 3 and 4 here now the important question is why did we do this lets see any number between 1 and 10 well have how many digits numbers like 35.5 9.8 they all have one digit to the left of the decimal point and if we look at the log scale we can say that if the number has one digit then its log will be between zero and one the logarithm will be of the form zero po