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This Problem is extremley confusing could someone help? Thank you so much for your time!

 Apr 12, 2020
 #1
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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

 Apr 12, 2020
 #2
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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!

 Apr 12, 2020

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