Use of Logarithms to Find the Product of Numbers with Exponents

b. Example 2. Find the fourth root of 625.

Solution.

Fourth root 625 = (625)1/4

log (625)1/4 = 1/4 log 625 = 1/4 X 2.7959 = 0.6990

antilog 0.6990 = 5.00

Thus, the fourth root of 625 = 5.00

1-42. USE OF LOGARITHMS TO FIND THE PRODUCT OF NUMBERS WITH

EXPONENTS

To find the product of a number that has an exponent, determine the logarithm of

the number and multiply by the exponent. The antilogarithm of the product is taken.

For example, if a number has been squared, find the logarithm of the number and

multiply by two, then find the antilog.

a. Example 1. Find the product of (625)2 using logarithms.

Solution.

log 6252 = 2 log 625 = 2 X 2.7959 = 5.5918

antilog 5.5918 = 391,000 = 3.91 X 105

NOTE:

If 625 is squared with a calculator, the resulting number is 390,625.

b. Example 2. Find the product of 62510 using logarithms.

Solution.

log 62510 = 10 log 625 = 10 X 2.7959 = 27.959

antilog 27.959 = 9.10 X 1027

1-43. EXERCISES, SECTION VI

After you have completed the following exercises, turn to the end of the lesson,

and check your answers with the solutions.

MD0837

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