Transformations (2)

Question

Which point satisfies both ƒ(x) = 2^x and g(x) = 3^x?

(0,1)

(0,-1)

(1,0)

(-1, 0)

Answer 1

The easy way to do it is to plug in the x-value of each point and see if you get the y-value. I'll do the last one, (-1, 0):

x 2^x 3^x

0

0

1

-1 2^-1 = 1/2 3^-1 = 1/3

Neither equation produced the correct y-value, which is 0. So (-1,0) satisfies neither equation. You try the other three points. Only one gives the correct y-value for both equations.

The other way to do it is to set the two equations equal and solve for x:

2^x = 3^x

log(2^x) = log(3^x)

x log(2) = x log(3)

Only one value of x can make the above equation true.