Question

Given log3 2=0.631 log3 7=1.771 what is log3 14?

Answer 1

In logarithm, inverse operations are applied.
$log_3{14} = log_3{7} + log_3{14} \\ log_3{14} = 0.631 + 1.771 \\log_3{14} = 2.402$

Answer 2

Answer:

$log_{3} 14 = 0.631 + 1.771 = 2.402$

Step-by-step explanation:

Logarithms have the following property:

$log_{a}(x*y)=log_{a}(x)+log_{a}(y)$

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:

$log_{3} (14)=log_{3} (2*7)$

Now we can use the property, replacing a by 3, x by 2, and y by 7, the we obtain:

$log_{a}(x*y)=log_{a}(x)+log_{a}(y)$

$log_{3}(7*2)=log_{3}(2)+log_{3}(7)$

The values of $log_{3}(2)$ and $log_{3}(7)$ are known, so the last step is to replace that values:

$log_{3}(7*2)=log_{3}(7)+log_{3}(2)$

$log_{3}(7*2)=0.631+1.771$

$log_{3}(7*2)=2.402$

At the end the value of $log_{3}(14)$ is 2.402