What is the solution to the equation 9^(x - 2) = 27 ?

x = 2.5
x = 0.5
x = -0.5
x = 3.5

Question

What is the solution to the equation 9^(x - 2) = 27 ?
 	
	x = 2.5
	x = 0.5
	x = -0.5
	x = 3.5

jim_thompson5910 · Answer

Hint: rewrite 9 as 3^2 and 27 as 3^3

jim_thompson5910 · Answer

Then you can say

9^(x - 2) = 27

(3^2)^(x - 2) = 3^3

3^(2(x-2)) = 3^3

anonymous · Answer

would the answer be...
x=2.5?

jim_thompson5910 · Answer

Check:

9^(x - 2) = 27

9^(2.5 - 2) = 27 ... plug in the *possible* solution x = 2.5

9^(0.5) = 27

3 = 27

The last equation is false, so x = 2.5 is NOT the answer

anonymous · Answer

ahh i'm still confused.

jim_thompson5910 · Answer

the bases are the same in 3^(2(x-2)) = 3^3

so the exponents are the same:  2(x-2) = 3

jim_thompson5910 · Answer

what do you get when you solve 2(x-2) = 3

anonymous · Answer

0...? i'm sorry. i'm really bad at math.

jim_thompson5910 · Answer

that's ok, you'll get better with practice

distribute to get 

2(x-2) = 3

2x-4 = 3

what's next?

anonymous · Answer

2x=7
x=7/2

anonymous · Answer

am i just plugging in the answer choices for x?

jim_thompson5910 · Answer

you can if you want to check (that's what I would do)

jim_thompson5910 · Answer

btw, x = 7/2 is the same as x = 3.5

anonymous · Answer

ohhh okay thank you so much.

anonymous · Answer

im so comfused I worked it out like this
9^(x-2)=27
3^2(x-2)=3^9
3^2x-4=3^9
2x-4=9
2x=13
13\2
x=6.5
but its not a choice. I have pluged in all of them and nothing im so condused. if anyone finds an answer please let me know

jim_thompson5910 · Answer

27 is NOT equal to 3^9

you're thinking of 3 times 9 = 27

-------------------------------------------------------

It should be 27 = 3^3

anonymous · Answer

its x=-0.5