SOLUTION: 5^(2x) - 5^(x-1) = -6

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 5^(2x) - 5^(x-1) = -6       Log On


   



Question 1055949: 5^(2x) - 5^(x-1) = -6

Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.
5^(2x) - 5^(x-1) = -6
~~~~~~~~~~~~~~~~~~~~~~~

This equation is the same as

5%5E%282x%29+-+%281%2F5%29%2A5%5Ex = -6.

Multiply both sides by 5. You will get.

5%2A%285%5E%282x%29%29+-+5%5Ex+%2B+30 = 0.

Introduce new variable u = 5%5Ex. Then the last equation takes the form

5u%5E2+-+u+%2B+30 = 0.

Apply the quadratic formula

u%5B1%2C2%5D = %281+%2B-+sqrt%281+-+4%2A5%2A30%29%29%2F10.

There are NO real solutions.

Are you sure you correctly wrote your equation?