Question

log 4  log 5  log 6  log 7  log 8  log 9 (

Answer 1

Step-by-step explanation:

Here, the given expression is,

(log_34) (log_4 5) (log_5 6) (log_6 7) (log_7 8) (log_8 9) (log_9 9)(log34)(log45)(log56)(log67)(log78)(log89)(log99)

By the logarithm property,

=\frac{log4}{log3}\times \frac{log5}{log4}\times \frac{log6}{log5}\times \frac{log7}{log6}\times \frac{log8}{log7}\times \frac{log9}{log8}\times \frac{log9}{log9}=log3log4×log4log5×log5log6×log6log7×log7log8×log8log9×log9log9

=\frac{log9}{log3}=log3log9

Again by logarithm property,

=log_39=log39

=log_3(3)^2=log3(3)2

=2log_3 3=2log33              

=2=2 ( log_a a = 1 )(logaa=1)