SOLUTION: (49/81)^x+1 > 9/7

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Question 1175919: (49/81)^x+1 > 9/7
Found 3 solutions by CubeyThePenguin, ankor@dixie-net.com, ikleyn:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%2849%2F81%29%5Ex%2B1+%3E+9%2F7
%2849%2F81%29%5Ex+%3E+9%2F7+-+7%2F7
%2849%2F81%29%5Ex+%3E+2%2F7
use natural logs
x%2Alog%2849%2F81%29+%3E+log%282%2F7%29
x > log%28%282%2F7%29%29%2Flog%28%2849%2F81%29%29
use your calc
x > 2.49242

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.

The  6-th sense tells me that the inequality is

            %2849%2F81%29%5E%28x%2B1%29 > 9%2F7. 

If so, then it is equivalent to

    %2881%2F49%29%5E%28-%28x%2B1%29%29 > 9%2F7

    %289%2F7%29%5E%28-2%28x%2B1%29%29 > 9%2F7



Since the base of the exponential function is greater than 1, it inplies

     -2(x+1) > 1

     -2x - 2 > 1

      -2 - 1 > 2x

       2x < -3                

        x < -3%2F2.             ANSWER


Visual  CHECK



    


       Plot y = %2849%2F81%29%5E%28x%2B1%29 (red)  and y = 9%2F7 (green)

Solved.