Question

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

Answer 1

hint:

9 = 3^2
27 = 3^3

does that help?

Answer 2

um kinda

Answer 3

x = 2.5
x = 3.5
x = 0.5
x = -0.5
are my answer choices

Answer 4

Can someone help me?

Answer 5

so apply my hint to the problem..

Answer 6

I don't understand? I thought it would be 5 but thats not a answer choice

Answer 7

or 27 = 9^(3/2)

Answer 8

9^3 = 729

Answer 9

okay so you have
\[\Large 9^ {x-2} = 27\]
apply my hint here (3^2 = 9; 3^3 = 27)
\[\Large \implies (3^2)^{x-2} = 3^3\]
does that help?

Answer 10

so 3x^-4 = 9?

Answer 11

i mean 3x^4 = 28

Answer 12

how did you get that?

Answer 13

3 times x = 3x and 2 times -2 is negative 4 and 3^3 is 27

Answer 14

why did you multiply 3 by x?

Answer 15

bevause x is on the outside of the parenthesis

Answer 16

hmm well you did something close to what was supposed to happen

you apply the rule
\[\large (a^m)^n = a^{mn}\]
so that means \[\Large (3^2)^{x-2} = 3^3\]
becomes\[\Large \implies 3^{2x - 4} = 3^3\]
got it?

Answer 17

kinda

Answer 18

so now use the rule \[\Large a^x = a^y \Longleftrightarrow x = y\]

Answer 19

so the answer is 3.5

Answer 20

sounds right

Answer 21

thanks for the help

Answer 22

welcome ^_^