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

`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