Answer:
[tex]log_{3} 14 = 0.631 + 1.771 = 2.402[/tex]
Step-by-step explanation:
Logarithms have the following property:
[tex]log_{a}(x*y)=log_{a}(x)+log_{a}(y)[/tex]
Taking into account the below property of logarithms, we can transform the initial problem in order to find a result. So we need to rewrite the exercise as:
[tex]log_{3} (14)=log_{3} (2*7)[/tex]
Now we can use the property, replacing a by 3, x by 2, and y by 7, the we obtain:
[tex]log_{a}(x*y)=log_{a}(x)+log_{a}(y)[/tex]
[tex]log_{3}(7*2)=log_{3}(2)+log_{3}(7)[/tex]
The values of [tex]log_{3}(2)[/tex] and [tex]log_{3}(7)[/tex] are known, so the last step is to replace that values:
[tex]log_{3}(7*2)=log_{3}(7)+log_{3}(2)[/tex]
[tex]log_{3}(7*2)=0.631+1.771[/tex]
[tex]log_{3}(7*2)=2.402[/tex]
At the end the value of [tex]log_{3}(14)[/tex] is 2.402
