Evaluating Logarithmic Equations

Question

How might I evaluate the logarithmic equation of:

25 = log₅(3-x) - 2 log₅(x)

Any help would be greatly appreciated!

Answer 1

You calculate 5^left side = 5^ right side.

We get

5^25 = (3-x)/x^2 or

5^25 x^2 = 3 - x

5^25 x^2 + x - 3 = 0

x = (-1 ±√(1 + 12*5^25))/(2*5^25)

As x must be positive, the solution is (-1 +√(1 + 12*5^25))/(2*5^25)