SOLUTION: Is the function exponential? K(x)=(9^x)/(sqrt((3)*8^x) If is an exponential function, transform the function into K(x)=ab^x. Find the values of a and b. Here's my calcula

Algebra ->  Exponents -> SOLUTION: Is the function exponential? K(x)=(9^x)/(sqrt((3)*8^x) If is an exponential function, transform the function into K(x)=ab^x. Find the values of a and b. Here's my calcula      Log On


   

Question 996094: Is the function exponential?
K(x)=(9^x)/(sqrt((3)*8^x)
If is an exponential function, transform the function into K(x)=ab^x. Find the values of a and b.
Here's my calculation and the steps I took but it I could not find the right answer.
(9^x)/sqrt((3)8^x)
9^x/3(1/3)8^x
a=(9/8)^x
b=3(1/2) or 1.5
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation, as best i can determine, is:

k(x) = 9^x / (sqrt(3) * 8^x)

this can be re-written as 9^x / 8^x * 1 / sqrt(3)

9^2 / 8^x can be rewritten as (9/8)^x, so the expression becomes:

1 / sqrt(3) * (9/8)^x

1 / sqrt(3) can be rewritten as sqrt(3)/3.

the expression becomes:

sqrt(3)/3 * (9/8)^x

a = sqrt(3)/3
b = (9/8)

ab^x becomes sqrt(3)/3 * (9/8)^x

the way to confirm it's accurate is to solve both the original equation and the final equation using the same value of x to see if the answer match.

the other way is to graph both equations.
if they're identical, they will show up as the same line on the graph.
line, in this case, can be curved line.

the graph of both equations is shown below:

you can see that both equations draw the same line on the graph which means the equations are identical.

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