Question

Choose one logarithmic property.
Use an exponential property to defend the validity of that specific logarithmic property. Show all work.

Answer 1

The logarithmic property chosen here is:

$log_{a}$ m - $log_{a}$ n = $log_{a}$ $\frac{m}{n}$, and its validity is proven below:

The logarithmic properties are up to six, but one of it that is applicable here is:

$log_{a}$ m - $log_{a}$ n = $log_{a}$ $\frac{m}{n}$

In the above expression, both the numerator and denominator have the same base number, but different powers. So in this case, dividing a number of power m by the same number but of power n would given an answer that is the same as the number to the power of the difference between m and n.

For example: Solve;

a. $log_{10}$ 6 - $log_{10}$ 3

b. $log_{10}$ 8 - $log_{10}$ 5

c. $log_{b}$ 6 - $log_{b}$ 2

Solutions:

a. $log_{10}$ 6 - $log_{10}$ 3 = $log_{10}$ $\frac{6}{2}$

        = $log_{10}$ 2

        = 0.3010

b. $log_{10}$ 8 - $log_{10}$ 5 = $log_{10}$ $\frac{8}{5}$

      = $log_{10}$ 1.6

       = 0.2041

c. $log_{b}$ 6 - $log_{b}$ 2 = $log_{b}$ $\frac{6}{2}$

        = $log_{b}$ 3

The stated examples defend the validity of the specific logarithmic property.

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