Question

(log3 4) (log4 5) (log5 6) (log6 7) (log7 8) (log8 9) (log9 9) = ?

Answer 1

By change of base.
--> Log3/log4 × Log4/log5 ×log5/log6 × log6/log7 × log7/log8 × log8/log9 × log9/log9
We get:

Log3/log9

Log 3 / log 3^2

Log3 /2 log 3 = 1/2


=1/2

Answer 2

Answer: 2

 

Step-by-step explanation:

Here, the given expression is,

$(log_34) (log_4 5) (log_5 6) (log_6 7) (log_7 8) (log_8 9) (log_9 9)$

By the logarithm property,

$=\frac{log4}{log3}\times \frac{log5}{log4}\times \frac{log6}{log5}\times \frac{log7}{log6}\times \frac{log8}{log7}\times \frac{log9}{log8}\times \frac{log9}{log9}$

$=\frac{log9}{log3}$

Again by logarithm property,

$=log_39$

$=log_3(3)^2$

$=2log_3 3$              

$=2$                                  $( log_a a = 1 )$