How do you solve #ln(x  3) + ln(x + 4) = 1#?
Now, that we have the domain we can solve the equation in this domain, thus:
We apply the quadratic formula,
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To solve the equation ln(x  3) + ln(x + 4) = 1, you can use the properties of logarithms to combine the two logarithmic terms into a single logarithm. Then, you can exponentiate both sides to eliminate the logarithm. After that, you can solve for x. Here are the steps:

Combine the logarithmic terms using the property: ln(a) + ln(b) = ln(a * b). ln(x  3) + ln(x + 4) = ln((x  3)(x + 4)).

Rewrite the equation: ln((x  3)(x + 4)) = 1.

Exponentiate both sides using the property of logarithms: e^ln(u) = u. e^ln((x  3)(x + 4)) = e^1.

Simplify: (x  3)(x + 4) = e.

Expand and rearrange the equation: x^2 + x  12  e = 0.

Solve the quadratic equation for x using the quadratic formula or factoring.

Once you find the solutions for x, check if they are valid by ensuring they satisfy the domain of the original logarithmic equation, which requires x > 3 and x > 4.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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