Lg25-lg(2x+3)=lg3-lg(x-9)

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To solve this equation, we will first use the property of logarithms that states lg(a) - lg(b) = lg(a/b).

So, the equation becomes:

lg(25) - lg(2x + 3) = lg(3) - lg(x - 9)

Now, we can combine the logs using the property mentioned above:

lg(25/(2x + 3)) = lg(3/(x - 9))

Now, we can remove the logarithms by setting the expressions inside the logarithms equal to each other:

25/(2x + 3) = 3/(x - 9)

Now, we can solve for x:

25(x - 9) = 3(2x + 3)
25x - 225 = 6x + 9
19x = 234
x = 12.3158

Therefore, the solution to the equation lg(25) - lg(2x + 3) = lg(3) - lg(x - 9) is x = 12.3158.