SOLUTION: SOLUTION: Write a power Function of the form y=ab^x whose graph passes through the given points: (2,4) (3,7)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: SOLUTION: Write a power Function of the form y=ab^x whose graph passes through the given points: (2,4) (3,7)       Log On


   

Question 849269: SOLUTION: Write a power Function of the form y=ab^x whose graph passes through the given points: (2,4) (3,7)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This may be a misunderstanding for the way in which you want the solution; but take logarithms of both sides:
log%28%28y%29%29=log%28%28ab%5Ex%29%29
log%28%28y%29%29=log%28%28a%29%29%2Bx%2Alog%28%28b%29%29
log%28%28y%29%29=x%2Alog%28%28b%29%29%2Blog%28%28a%29%29
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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%28%284%29%29=2%2Alog%28%28b%29%29%2Blog%28%28a%29%29
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log%28%287%29%29=3%2Alog%28%28b%29%29%2Blog%28%28a%29%29
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Solving this system first eliminating log(a), you find log%28%28b%29%29=log%28%287%29%29-log%28%284%29%29.
Continuing using substitution you find log%28%28a%29%29=log%28%287%29%29%2B3%2Alog%28%284%29%29-3%2Alog%28%287%29%29

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%28highlight%28y=%281.3311%29%281.75%29%5Ex%29%29