How do you solve #ln2-ln(3x+2)=1#?
In order to solve this logarithmic equation, we can make use of the properties of logarithms, such as
We can now rewrite this equation as follows:
So our equation now has become a lot more appealing:
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To solve the equation ln(2) - ln(3x + 2) = 1:
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Combine the logarithms using the property that ln(a) - ln(b) = ln(a/b).
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Rewrite the equation as a single logarithmic expression.
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Use the property of logarithms that ln(e) = 1 to simplify.
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Solve for the variable ( x ) by isolating it on one side of the equation.
Here are the steps in detail:
ln(2) - ln(3x + 2) = 1
ln(2 / (3x + 2)) = 1
2 / (3x + 2) = e^1
2 / (3x + 2) = e
Now, cross multiply:
2 = e(3x + 2)
Divide both sides by ( e ):
2 / e = 3x + 2
Now, isolate ( x ) by subtracting 2 from both sides:
(2 / e) - 2 = 3x
Finally, divide both sides by 3:
[ x = \frac{(2 / e) - 2}{3} ]
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When evaluating a one-sided 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 one-sided 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 one-sided 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 one-sided 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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