Question 477461
<pre>
We are given:

{{{a^2=b^3=c^5=d^6}}}

Take logs base d: 

{{{log(d,a^2)=log(d,b^3)=log(d,c^5)=log(d,d^6)}}}

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

{{{2log(d,a)=3log(d,b)=5log(d,c)=6log(d,d)}}}

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

{{{2log(d,a)=3log(d,b)=5log(d,c)=6(1)}}}

{{{2log(d,a)=3log(d,b)=5log(d,c)=6}}}

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

 {{{2log(d,a)=6}}}

Divide both sides by 2

 {{{log(d,a)=3}}}

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 {{{3log(d,b)=6}}}

Divide both sides by 3

 {{{log(d,b)=2}}}

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 {{{5log(d,c)=6}}}

Divide both sides by 5

 {{{log(d,c)=6/5}}}

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

{{{ log( d , abc) = log(d,a)+log(d,b)+log(d,c)  = 3+2+6/5=5+6/5=25/5+6/5=31/5  }}}

Edwin</pre>