log.052/log.94 what is the answer

Answer 1

If you are not allowed to use a calculator, you may have to do it by hand, using mantissas and characteristics. I will show you the steps for one of the numbers.

(1) Express each number in standard exponential notation.

0.052 = 5.2 x 10^-2

(2) Take log₁₀ of the number.

log(5.2 x 10^-2) = log5.2 + log(10^-2) = log5.2 - 2

Note that -2 is just the power of 10 when the number is in standard exponential notation. This quantity, with its correct sign, is called the characteristic.

(3) Find log5.2 in a table of base 10 logarithms (also called common logarithms). The log that you find is called the mantissa.

(4) log(0.052) = (mantissa) + (characteristic) = mantissa - 2

Do the same for 0.94, and note its characteristic is -1. Find the mantissa for 9.4.

log0.94 = mantissa - 1

Plug the results into your stated problem.