In(x^-6x+9)=in3+in(x+3)

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вопрос

First, we need to simplify the expression ln(x^2 - 6x + 9) on the left side:

Since x^2 - 6x + 9 can be factored into (x - 3)(x - 3), we can rewrite ln(x^2 - 6x + 9) as ln((x - 3)^2).

Next, we can use the property of logarithms that ln(a^b) = bln(a) to rewrite ln((x - 3)^2) as 2ln(x - 3).

Therefore, the left side becomes 2*ln(x - 3).

Now, we have: 2*ln(x - 3) = ln(3) + ln(x + 3).

We can combine the two logarithms on the right side using the property ln(a) + ln(b) = ln(a*b):

2*ln(x - 3) = ln(3(x + 3)).

Now, we have the equation:

2*ln(x - 3) = ln(3(x + 3)).

This equation can be solved by comparing the arguments of the logarithms on both sides.