SOLUTION: 1. Solve the following equations a) 5^(2x) + 5^(x) - 6 = 0 (hint let y = 5^(x) Can you please help me out? Thanks so much in advance:) Can you please show all the steps it wou

Question 744487: 1. Solve the following equations
a) 5^(2x) + 5^(x) - 6 = 0 (hint let y = 5^(x)
Can you please help me out? Thanks so much in advance:)
Can you please show all the steps it would really help me understand:)
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
a) 5^(2x) + 5^(x) - 6 = 0 (hint let y = 5^(x)
.
We Let y = 5^x
if so, we can rewrite:
5^(2x) + 5^(x) - 6 = 0
AS
y^2 + y - 6 = 0
now, we factor :
(y+3)(y-2) = 0
y = {-3, 2)
.
But, we still need to find x:
since
y = 5^x
we substitute each value of y to find x:
-3 = 5^x

since we can't take the log of a negative value we throw out this solution.
.
2 = 5^x

0.431 = x

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