SOLUTION: Write down the equation of the graph of the exponential function of the form y=a^x which passes through the point (1,2). y=5^x The co-ordinates given are (1,2) and (1,5) I

Question 927408: Write down the equation of the graph of the exponential function of the form y=a^x which passes through the point (1,2).
y=5^x
The co-ordinates given are (1,2) and (1,5)
I had a similar question;
"Write down the equation of the graph of the exponential function of the form y=a^x which passes through the point (2,4)."
In that question, y=5^x and the points given were (2,9) and (2,4)
I identified the answer as y=2^x.
I thought if y=2^x and y=4; then 2^2; then 3^2.
Can anyone please help me identify the correct technique?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe that this tutorial will help you with what you are looking for.

https://www.youtube.com/watch?v=KVEPO2gn2R8

the general form of the exponential equation is y = ab^x.

i don't think coordinates of (1,2) and (1,5) will lead to a good solution because what you are stating is that ab^1 = 5 and ab^1 = 2

if i solve this equation for a, i will get:

a = 5/b^1 and a = 2/b^1

if i set these equations equal to each other, i get:

5/b^1 = 2/b^1

if i cross multiply, i get:

5b^1 = 2b^1

if i divide both sides of the equation by b^1, i will get:

5 = 2 which is not true and so the points you are using for a reference are not valid.

check out the tutorial and see if that meets your needs.

it discusses how to solve exponential equations when given 2 points.

the procedure is what i just showed you in a little bit more detail with some more examples.

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