SOLUTION: Hello, I was wondering if you may be able to help me with this problem, I've tried applying what I know, but it doesn't seem to come out right... (1/9)^3x=27 So what I've tried

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, I was wondering if you may be able to help me with this problem, I've tried applying what I know, but it doesn't seem to come out right... (1/9)^3x=27 So what I've tried      Log On


   



Question 615239: Hello, I was wondering if you may be able to help me with this problem, I've tried applying what I know, but it doesn't seem to come out right...
(1/9)^3x=27
So what I've tried is...
1. Setting the bases equal
So, basically,
3^2(-3x)=3^3
**I did (-3x) because it's under a 1 in the original problem, I feel that this may be where I am having issues.
2.Solve for X.
2(-3x)=3
-6x=3
x=-2
However when I try to check my work, the problem just doesn't seem to come out right with X being -2. I would greatly appreciate your time and help! Many regards, -Sarah.

Found 3 solutions by Earlsdon, Alan3354, josmiceli:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You've done everything correctly except the final step:
You had:
-6x+=+3
x+=+-2
What it should be is:
-6x+=+3 Divide both sides by -6.
x+=+-%283%2F6%29 Simplify.
x+=+-%281%2F2%29
Check this out as a solution!

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F9%29%5E%283x%29=27+
%283%5E-2%29%5E%283x%29+=+3%5E3
3%5E%28-6x%29+=+3%5E3
-6x = 3
x = -1/2
----------
You had it right, except for the last step

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%281%2F9%29%5E3x=27+
Note That +1%2F9+=+%281%2F3%29%5E2+, so
+%281%2F9%29%5E%283x%29+=+27+
+%28%281%2F3%29%5E2%29%5E%283x%29+=+3%5E3+
+%28+1%2F3+%29%5E%286x%29+=+3%5E3+
I can take the cube root of both sides
+%281%2F3%29%5E%282x%29+=+3+
+%28+1%2F3+%29%5E%282x%29+=+%281%2F3%29%5E%28-1%29+
+2x+=+-1+
+x+=+-1%2F2+
-----------
check:
+%281%2F9%29%5E3x=27+
+%281%2F9%29%5E%283%2A%28-1%2F2%29%29=27+
+%281%2F9%29%5E%28-3%2F2%29+=+3%5E3+
+%28%281%2F3%29%5E2%29%5E%28-3%2F2%29+=+3%5E3+
+%281%2F3%29%5E%28-3+%29+=+3%5E3+
+1+%2F+%281%2F3%29%5E3+=+3%5E3+
+3%5E3+=+3%5E3+