document.write( "Question 979068: How do I solve-
\n" ); document.write( "If 2^a=3^b=6^c, show that c=ab/a+b.
\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #600450 by KMST(5328) $\"\"$ $\"About$

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2^a=6^c ---> (2^a)^(b/a+b)=(6^c)^(b/a+b) ---> 2^(ab/(a+b))=6^(cb/(a+b))
\n" ); document.write( "3^b=6^c ---> (3^b)^(a/a+b)=(6^c)^(a/a+b) ---> 3^(ab/(a+b))=6^(ca/(a+b))
\n" ); document.write( "Then, multiplying
\n" ); document.write( "[ 2^(ab/(a+b)) ] [ 3^(ab/(a+b)) ] = [ 6^(cb/(a+b)) ] [ 6^(ca/(a+b)) ]
\n" ); document.write( "(2*3)^(ab/(a+b)) = 6^[ cb/(a+b) + ca/(a+b) ]
\n" ); document.write( "6^(ab/(a+b)) = 6^[(cb+ca)/(a+b)]
\n" ); document.write( "6^(ab/(a+b)) = 6^[c(b+a)/(a+b)]
\n" ); document.write( "6^(ab/(a+b)) = 6^c ------> ab/(a+b) = c \n" ); document.write( "

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