Question

Applying the concepts. Need help finding the value.

Answer 1

we can use formula

`log_ab=(ln(b))/(ln(a))`

`log_23*log_34*log_45*log_56*log_6 7 *log_7 8=(ln(3))/(ln(2))*(ln(4))/(ln(3))*(ln(5))/(ln(4))*(ln(6))/(ln(5))*(ln(7))/(ln(6))*(ln(8))/(ln(7))`

now, we can cancel terms

and then we can simplify it

`log_23*log_34*log_45*log_56*log_6 7 *log_7 8=(ln(8))/(ln(2))`

`log_23*log_34*log_45*log_56*log_6 7 *log_7 8=(ln(2^3))/(ln(2))`

`log_23*log_34*log_45*log_56*log_6 7 *log_7 8=(3ln(2))/(ln(2))`

now, we can simplify it

and we get

`log_23*log_34*log_45*log_56*log_6 7 *log_7 8=3`...........Answer