SOLUTION: If{{{a^2=b^3=c^5=d^6}}}, then prove {{{ log( d , abc = 31/5 ) }}}

Question 477461: If, then prove

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

We are given:



Take logs base d: 



Use the rule of logs that says the log of an exponential is
the exponent times the log of the base of the exponent:



Use the rule of logs on that last expression that says 
the log of the base of the log is always equal to 1:





Set each of the 3 expressions = 6 and solve for the logs:

 

Divide both sides by 2

 

--------------------

 

Divide both sides by 3

 

--------------------

 

Divide both sides by 5

 

--------------------

Use the rule of logs that says the log of a product 
equals the sum of the logs of the factors: 



Edwin

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