SOLUTION: Solve for x (1/7)^x=49

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Question 80419: Solve for x
(1/7)^x=49
Found 2 solutions by josmiceli, Earlsdon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F7%29%5Ex+=+49
note that
49+=+7%5E2
so
%281%2F7%29%5Ex+=+7%5E2
also note
%281%2F7%29%5Ex+=+1%2F%287%5Ex%29
now I have
1%2F%287%5Ex%29+=+7%5E2
You should know that
1%2F%287%5Ex%29+=+7%5E%28-x%29
now I have
7%5E%28-x%29+=+7%5E2
-x+=+2
x+=+-2 answer

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%281%2F7%29%5Ex+=+49 But 49+=+7%5E2 = 1%2F7%5E%28-2%29+=+%281%2F7%29%5E-2, so we get:
%281%2F7%29%5Ex+=+%281%2F7%29%5E-2, therefore x = -2
If you are not comfortable with this approach, here's another one:
%281%2F7%29%5Ex+=+49 Take the logarithm of both sides.
Log%5B10%5D%281%2F7%29%5Ex+=+Log%5B10%5D%2849%29 Apply the power rule to the left side.
x%2ALog%5B10%5D%281%2F7%29+=+Log%5B10%5D%2849%29 Divide both sides by Log%5B10%5D%281%2F7%29
x+=+%28Log%5B10%5D%2849%29%29%2FLog%5B10%5D%281%2F7%29 Do this with your calculator.
x+=+-2