Question

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

Answer 1

Use the quotient rule [ $\text{log}_a\frac{x}{y} = \text{log}_ax-\text{log}_ay$ ] to simplify.

$\text{log}\frac{5}{7} = \text{log}(5)-\text{log}(7)$

Simplify using the given values.

0.6990 - 0.8451

-0.1461

Therefore, $\text{log}\frac{5}{7}=-0.1461$

Best of Luck!

Answer 2

Answer: Option a.

Step-by-step explanation:

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

 $log(a)-log(b)=log(\frac{a}{b})$

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

$log(\frac{5}{7})=log(5)-log(7)$

You know that:

$log5=0.6990\\log7=0.8451$

Then, when you substitute values, you obtain:

$0.6990-0.8451=-0.1461$