Suppose 
for some positive integers k,b. Find all possible values of k + b.
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here b=4 and k=4
then k+b=8
then k+b=8
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Solution :
Given k , b are positive integers.
3^k × b² = 6⁴
=> b² = 6⁴/3^k
=> b = √( 6⁴/3^k )
=> b = 6²/√3^k
i ) if k = 2 then b = 6²/√3^2= 36/3 = 12
( k , b ) = ( 2 , 12 )
k + b = 2 + 12 = 14
ii ) if k = 4 then
b = 6²/√3⁴
=> b = 36/9 = 4
( k , b ) = ( 4 , 4 )
k + b = 4 + 4 = 8
••••
Given k , b are positive integers.
3^k × b² = 6⁴
=> b² = 6⁴/3^k
=> b = √( 6⁴/3^k )
=> b = 6²/√3^k
i ) if k = 2 then b = 6²/√3^2= 36/3 = 12
( k , b ) = ( 2 , 12 )
k + b = 2 + 12 = 14
ii ) if k = 4 then
b = 6²/√3⁴
=> b = 36/9 = 4
( k , b ) = ( 4 , 4 )
k + b = 4 + 4 = 8
••••
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