Question

Find the X-intercept
f(x)=3^(x-1)-2

Answer 1

Hello!

The answer is:

The function intercepts de x-axis at "x" equal to 1.631.

Why?

To find the x-intercept of the function, we need to make f(x) or "y" equal to 0, and then, isolate "x".

So, isolating we have:

`f(x)=3^((x-1)) -2\\\\0=3^((x-1)) -2\\\\3^((x-1))=2\\\\Log_(3)(3^((x-1)))=Log_(3)(2)\\\\x-1=0.631\\\\x=0.631+1=1.631`

Hence, we have that the function intercepts de x-axis at "x" equal to 1.631.

Have a nice day!

Note: I have attached a picture for better understanding.