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Answer
The solution is
.
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To solve the equation
, we can start by simplifying it.
First, recall the property of logarithms that states
. Therefore, we can rewrite the left side:
Now, the equation becomes:
Since the logarithms are equal, we can set the arguments equal to each other (assuming
):
Multiplying both sides by
(and assuming
) gives us:
Now, rearranging the equation:
Factoring gives:
The quadratic
has no real solutions, as its discriminant
. Therefore, the only real solution is
.
Let’s verify:
If
:
The solution to the equation is
.