The value of (log2(3))(log3(4))(log4(5))(log5(6))(log6(7))(log7(8)) is equal to;

A) 2

B) 4

C) log7(8)

D) log2(7)

E) 3

### 1 Answer | Add Yours

According to logarithm;

`log_ab = (log_kb)/(log_ka)`

If we consider k = 10 which is log in base 10 then;

`log_ab = (logb)/(loga)`

Similarly we can write;

`(log2(3))(log3(4))(log4(5))(log5(6))(log6(7))(log7(8))`

`= (log3)/(log2)xx(log4)/(log3)xx(log5)/(log4)xx........(log7)/(log6)xx(log8)/(log7)`

`= (log8)/(log2)`

`= (log2^3)/(log2)`

`= (3log2)/(log2)`

`= 3`

*So the answer is 3. Correct answer is given at option E)*

**Sources:**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes