Question

Use the laws of logarithms and the values given below to evaluate the logarithmic expression (picture provided)

Answer 1

Use the quotient rule [
`\text{log}_a(x)/(y) = \text{log}_ax-\text{log}_ay` ] to simplify.

`\text{log}(5)/(7) = \text{log}(5)-\text{log}(7)`

Simplify using the given values.

0.6990 - 0.8451

-0.1461

Therefore,
`\text{log}(5)/(7)=-0.1461`

Best of Luck!

Answer 2

Answer: Option a.

Explanation:

To solve the given exercise, you must keep on mind the law of logarithms shown below:

`log(a)-log(b)=log((a)/(b))`

Therefore, by applying the law , you can rewrite the expression given, as following:

`log((5)/(7))=log(5)-log(7)`

You know that:

`log5=0.6990\\log7=0.8451`

Then, when you substitute values, you obtain:

`0.6990-0.8451=-0.1461`