SOLUTION: solve the exponential equation by using the property that bx = by implies x = y, for b> 0 and b ≠ 1 27^1/3x=(1/9)^2x-1

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Question 1088326: solve the exponential equation by using the property that bx = by implies x = y, for b> 0 and b ≠ 1
27^1/3x=(1/9)^2x-1
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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solve the exponential equation by using the property that bx = by implies x = y, for b> 0 and b ≠ 1
27^1/3x=(1/9)^2x-1
~~~~~~~~~~~~~~~~~~~~~~~ 

1.  Before solving this problem, let me say you that the formulation in the post is not correct.

    The correct formulation, PROBABLY, is THIS:

 
       solve the exponential equation by using the property that b^x = b^y implies x = y, for b> 0 and b ≠ 1

       27^1/3x=(1/9)^2x-1


    (By saying PROBABLY, I am actually 120% sure).


2.  Now the solution:

    27^((1/3)*x) = (1/9)^(2x-1)  ====>

    3*(3*(1/3)*x) = (1/3)^(2*(2x-1))  ====>

     =   ====>

     =   ====>

     x = -4x + 2  ====>  5x = 2  ====>  x =  = 0.4.

Answer. x = = 0.4.



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