SOLUTION: how do i solve (1/36)^x-1 =1296^2x

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Question 755750: how do i solve (1/36)^x-1 =1296^2x
Found 2 solutions by Edwin McCravy, MathLover1:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2F36%29x-2 = 12962x

Write 1296 as 362
Write 1%2F36 as 36-1

(36-1)x-2 = (362)2x

Remove the parentheses by multiplying the exponents:

36-x+2 = 364x

Since the base 36 is positive and not 1, we may drop the
36's and set their exponents equal to each other:

-x+2 = 4x
 -5x = -2
   x = %28-2%29%2F%28-5%29
   x = 2%2F5

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2F36%29%5E%28x-1%29+=1296%5E%282x%29.......write %281%2F36%29%5Ex-1 as 36%5E%281-x%29 and 1296 as 36%5E2
36%5E%281-x%29+=%2836%5E2%29%5E%282x%29 .........since %2836%5E2%29%5E%282x%29=%2836%29%5E%284x%29 we have

36%5E%281-x%29+=36%5E%284x%29..since bases same, exponents are same too; so, we have

1-x+=4x....solve for x

1=4x%2Bx

1=5x

1%2F5=x