25^x + 10*5^(x-1) -3 = 0

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To solve this equation, we need to first identify if there's a common base we can use to simplify the equation. In this case, we can rewrite the equation as:

25^x + 10(5^x)(5^-1) - 3 = 0

Now we can simplify further:

25^x + 10(5^x)(1/5) - 3 = 0
25^x + 2*5^x - 3 = 0

Let y = 5^x. Now we can rewrite the equation as:

25^x + 2*(5^x) - 3 = 0
y^2 + 2y - 3 = 0

Now we have a quadratic equation in terms of y. We can solve this equation using the quadratic formula:

y = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the values a = 1, b = 2, c = -3 into the quadratic formula:

y = (-2 ± sqrt(4 + 12)) / 2
y = (-2 ± sqrt(16)) / 2
y = (-2 ± 4) / 2

Therefore, the solutions for y are:

y = (2 + 4) / 2 = 6 / 2 = 3
y = (2 - 4) / 2 = -2 / 2 = -1

Now that we have the values for y, we can substitute back in to find the values for x:

For y = 3:
5^x = 3
x = log base 5 of 3

For y = -1:
5^x = -1
This solution is not possible because a negative number cannot be raised to a positive power in this context.

Therefore, the solution to the equation is:
x = log base 5 of 3