# 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

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Expert Answers

jeew-m | Certified Educator

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)*

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