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

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

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

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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