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.