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

1 Answer
Nov 17, 2016

(0, 1)

Explanation:

If f(x) = y = g(x) then we have:

2^x = 3^x

Divide both sides by 2^x to get:

1 = 3^x/2^x = (3/2)^x

Any non-zero number raised to the power 0 is equal to 1. Hence x=0 is a solution, resulting in:

f(0) = g(0) = 1

So the point (0, 1) satisfies y = f(x) and y = g(x)

Note also that since 3/2 > 1, the function (3/2)^x is strictly monotonically increasing, so x=0 is the only value for which (3/2)^x = 1