Log

If log3 𝑥 = 𝑡, use the law of logarithms to show that log3 √27 𝑥 is equivalent to 𝑡 + 3 2 .

                               log₃ sqrt 27 x =         =    log₃ x    +   log₃sqrt 27

                                                               =   t   + log₃   27 ^(1/2)

                                                               =  t +    log₃ ( 3³)^1/2

                                                                                     =  t +    log₃ 3^3/2

                                                                                    =  t + 3/2