Question

Log(2)3log(3)5log(5)6log(6)8=

Answer 1

$log_23\cdot log_35\cdot log_56\cdot log_68= \frac{log_35}{log_32}\cdot \frac{log_68}{log_65}=\\\\=log_25\cdot log_58=\frac{log_58}{log_52}=log_28=log_22^3=3\\\\\\Formyla:\; \; log_{a}{b}=\frac{log_{c}b}{log_{c}a}\; \; \Rightarrow\; \; \frac{log_{c}b}{log_{c}a}=log_ab$