Question

How do you show that `\log _ { 6} 7= \frac { \log _ { 2} 7} { 1+ \log _ { 2} 3}`?

Answer 1

`LHS=log_6 7`

`=log_2 7xxlog_6 2`

`=log_2 7/log_2 6`

`=log_2 7/log_2 (2xx3)`

`=log_2 7/(log_2 2+log_2 3)`

`=log_2 7/(1+ log_2 3)=RHS`