Which value of 𝑥 gives the same value of 𝑦 in both functions?

Question

The graphs of 𝑦=2^x and 𝑦=(1/2)^x.

Which value of 𝑥 gives the same value of 𝑦 in both functions?

𝑥=12

There is no value of 𝑥 which gives the same value of 𝑦 in both functions.

𝑥=2

𝑥=0

Answer 1

The y values are the same when 2^x = (1/2)^x.

2^x = (2^-1)^x So, 2^x = 2^-x. Therefore, x = -x. So, x = 0.

Answer 2

2^x = (1/2)^x

2^x = [(2^-1]^x

2^x = 2^-x

x = -x

Solution?