Please Help

Write each log as a common log:

   log₂(x)   =  log(x) / log(2)

   log₃​(x)   =  log(x) / log(3)

   log₄(x)   =  log(x) / log(4)

   log₅(x)   =  log(x) / log(5)

On the left-hand side, we will end with:  [ log(x) ]⁴  /  [ log(2) · log(3) · log(4) · log(5) ]

On the right-hand side, we will need to multiply each term by an appropriate term to get the common denominator

of [ log(2) · log(3) · log(4) · log(5) ].

Multiply the first term by  log(5) / log(5)

        the second term by  log(4) / log(4)

            the third term by  log(3) / log(3)

          the fourth term by  log(2) / log(2)

Adding those terms together, you will end with the numerator of  [ log(x) ]³ · [ log(2) + log(3) + log(4) + log(5) ]

Setting the two numerators together:  [ log(x) ]⁴  =  [ log(x) ]³ · [ log(2) + log(3) + log(4) + log(5) ]

Dividing out  [ log(x) ]³ , we get  log(x)  =  log(2) + log(3) + log(4) + log(5)

                                                   log(x)  =  log(120)

                                                         x   =   120

HI, Thank you for the response and explaing your method but I think your answer is incorrect. I am going to giv.e the problem another shot using your techniques. I really appreciate the help!