Answer:The value of given expression [tex]log_7343[/tex] is 3. Step-by-step explanation: Given: [tex]log_7343[/tex]We have to find the value of given expression [tex]log_7343[/tex]Consider the given expression [tex]log_7343[/tex]Rewrite 343 in base- power form as [tex]343=7^3[/tex]We have [tex]=\log _7\left(7^3\right)[/tex]Apply log rule, [tex]\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]We have , [tex]\log _7\left(7^3\right)=3\log _7\left(7\right)[/tex]Again Apply log rule [tex]\log _a\left(a\right)=1[/tex]we have [tex]\log _7\left(7\right)=1[/tex]Thus, [tex]3\log _7\left(7\right)=3[/tex]Thus, the value of given expression [tex]log_7343[/tex] is 3.