Question

Log 4 base 3 log 5 base 4 log 6 base 5 log 7 base 6 log 8 base 7 log 9 base 8 is

Answer 1

Above photo shows the answer and using log formulae, the answer is 2.

Answer 2

Answer:

$log_3\,4\times log_4\,5\times log_5\,6\times log_6\,7\times log_7\,8\times log_8\,9=2$

Step-by-step explanation:

Given: $log_3\,4\times log_4\,5\times log_5\,6\times log_6\,7\times log_7\,8\times log_8\,9$

We have to simplify.

we use the following results,

$log_a\,b=\frac{log\,b}{log\,a}\:\:and\:\:log\,a^b=blog\,a$

Consider,

$log_3\,4\times log_4\,5\times log_5\,6\times log_6\,7\times log_7\,8\times log_8\,9$

$\implies\frac{log\,4}{log\,3}\times\frac{log\,5}{log\,4}\times\frac{log\,6}{log\,5}\times\frac{log\,7}{log\,6}\times\farc{log\,8}{log\,7}\times\frac{log\,9}{log\,8}$

$\implies\frac{1}{log\,3}\times\frac{1}{1}\times\frac{1}{1}\times\frac{1}{1}\times\frac{1}{1}\times\frac{log\,3^2}{1}$

$\implies\frac{1}{log\,3}\times2log\,3$

$\implies2$

Therefore, $log_3\,4\times log_4\,5\times log_5\,6\times log_6\,7\times log_7\,8\times log_8\,9=2$