SOLUTION: f(x) = 5^4x + 20.5^2x solve the equation f(x) - 125 = 0

Algebra ->  Equations -> SOLUTION: f(x) = 5^4x + 20.5^2x solve the equation f(x) - 125 = 0      Log On


   

Question 1098171: f(x) = 5^4x + 20.5^2x
solve the equation f(x) - 125 = 0
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
For your info:  the multiplication sign is  ' * ',  and not the  dot   '.'


So, rewrite your post accordingly to avoid misunderstanding and ambiguity.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Combining the two pieces of given information, we have

5%5E%284x%29+%2B+20%2A5%5E%282x%29+-+125%29+=+0

Since %285%5E%282x%29%29%5E2+=+5%5E%284x%29, this is simply a "quadratic" equation, where the "variable" is 5%5E%282x%29. Factoring,

%285%5E%282x%29%2B25%29%2A%285%5E%282x%29-5%29+=+0
5%5E%282x%29+=+-25 or 5%5E%282x%29+=+5

The first of these gives no solution for x; the second one gives us
5%5E%282x%29+=+5+=+5%5E1
2x+=+1
x+=+1%2F2

Solution: x = 1/2