Question 849269
This may be a misunderstanding for the way in which you want the solution; but take logarithms of both sides:

{{{log((y))=log((ab^x))}}}
{{{log((y))=log((a))+x*log((b))}}}
{{{log((y))=x*log((b))+log((a))}}}
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Next, choose the base you want for those logarithms, either e or 10, or whatever you best want; and use the points given, to make two linear equations.


SYSTEM:
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{{{log((4))=2*log((b))+log((a))}}}
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{{{log((7))=3*log((b))+log((a))}}}
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Solving this system first eliminating log(a), you find {{{log((b))=log((7))-log((4))}}}.
Continuing using substitution you find {{{log((a))=log((7))+3*log((4))-3*log((7))}}}


Like I said, you need to choose a base for these logarithms, and get values for log(b) and log(a), and then find antilogs of them.  



Base 10 logarithms gives these:
log(b)=0.243038, b=1.75.
log(a)=0.12422, a=1.3311
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Equation: {{{highlight(highlight(y=(1.3311)(1.75)^x))}}}