f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b
Set up both equations with values
When x = 3, f(3) = 17, so we have a(b)^3 = 17
When x = 7, f(7) = 3156, so we have a(b)^7 = 3156
Isolate a in each equation
a = 17/(b)^3
a = 3156/(b)^7
Now set them equal to each other
17/(b)^3 = 3156/(b)^7
Cross Multiply
17b^7 = 3156b^3
Divide each side by b^3
17b^4 = 3156
Divide each side by 17
b^4 = 185.6471
b = 3.6912
Set up both equations with values
When x = 3, f(3) = 17, so we have a(b)^3 = 17
When x = 7, f(7) = 3156, so we have a(b)^7 = 3156
Isolate a in each equation
a = 17/(b)^3
a = 3156/(b)^7
Now set them equal to each other
17/(b)^3 = 3156/(b)^7
Cross Multiply
17b^7 = 3156b^3
Divide each side by b^3
17b^4 = 3156
Divide each side by 17
b^4 = 185.6471
b = 3.6912