Question

Solve xlog(base 3)x=81x^3

Answer 1

Given: x^ ( log(base 3)x ) = 81 x^3

To find: Solve the above question.

Solution:

• As we have given both sides x, and the rest terms in the powers, so lets take log with base 3 on both sides, we get:

              log (base 3) {x^ ( log(base 3)x ) }= log( base 3) 81 x^3

              {log (base 3) x }^2 = 3 log( base 3) x + 4{ log( base 3) 3}

              {log (base 3) x }^2 = 3 log( base 3) x + 4

• Now, replace log (base 3) x by y, we get:

               y^2 =  3y + 4

                y^2 - 3y - 4 = 0

• simplifying it, we get:

             (y-4) x (y+1) = 0

              y = 4, -1

• Now replace y with log (base 3) x

            log (base 3) x = 4, log (base 3) x = -1

            x = 3^4 , 1/3

Answer:

               So the value of x is 3^4 , 1/3.