Question

g(x) = 2^(x - 1) - 2
Find the x-intercept

I know the x-intercept is when y is zero, but I'm still unclear on the steps. Can someone help me out?

Answer 1

in this case g(x) is y, and you g(x)=0
\[ 2^{(x-1)} -2 = 0 \]
any idea what the next step should be ?

Answer 2

Eek, I have a feeling that I do but I'm not sure!

Answer 3

add 2 to both sides. can you do that ?

Answer 4

I did and got 2 when I added 0+2, is that it?

Answer 5

like this
\[ 2^{(x-1)} -2+2 = 0+2\]

Answer 6

Oooh I see, I added +2 to the first 2 in it!

Answer 7

on the left side -2 + 2 simplifies to 0
on the right side 0+2 is 2

\[ 2^{(x-1)} = 2\]

Answer 8

2 can be written as \( 2^1 \)

so we could write the equation as
\[ 2^{(x-1)} = 2^1\]

Answer 9

when the bases are equal (and here the base is 2 on both sides), you can set the exponents equal.

Answer 10

Thank you for clearing that bit up!

Answer 11

can you finish ?

Answer 12

I think I need a little help finishing, but I definitely understand the steps now

Answer 13

set the exponents equal
x-1 = 1

What is a good thing to add (to both sides) that makes the -1 next to the x add up to 0?

Answer 14

1?

Answer 15

Yes.

Answer 16

Thank you both!

Answer 17

you should get
x-1+1 = 1+1
or after simplifying
x = 2