What is the value of log 3 81 ?

Answer: [tex]\log _3\left(81\right)=4[/tex]Step-by-step explanation:Given : [tex]\log _3\left(81\right)[/tex]We have to find the value of [tex]\log _3\left(81\right)[/tex]Consider [tex]\log _3\left(81\right)[/tex]Rewrite 81 in base power form, [tex]81=3^4[/tex][tex]=\log _3\left(3^4\right)[/tex][tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]We have,[tex]\log _3\left(3^4\right)=4\log _3\left(3\right)[/tex][tex]=4\log _3\left(3\right)[/tex][tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex][tex]\log _3\left(3\right)=1[/tex][tex]=4\log _3\left(3\right)=4[/tex]Thus,  [tex]\log _3\left(81\right)=4[/tex]