To solve this equation, we can first use the property of logarithms that states log(a^b) = b*log(a).

Using this property, we can rewrite the equation as:

25 * log(5+x) = log(2x)

Now, we can use the property of logarithms that states log(a) + log(b) = log(ab) to combine the logarithms on the left side of the equation:

log((5+x)^25) = log(2x)

Now, we can set the expressions inside the logarithms equal to each other:

(5+x)^25 = 2x

Now, we can solve for x. This is a transcendental equation and cannot be solved algebraically. Some numerical methods like Newton's method or trial and error can be used to find an approximate solution for x.