How do you solve #Log(x+2)+log(x1)=1#?
The basic approach to solving log equations it to get them into simplest form and then put them back into exponential form.
In the case of this problem, the log expressions are not as simple as possible and you need to use your log rules to combine the two expressions. Because there is not base written with LOG the base is assumed to be 10.
put the equation back into exponential form:
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Assuming the base of the logarithm is 10, the answer is 3.
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To solve the equation ( \log(x+2) + \log(x1) = 1 ):

Combine the logarithms using the product rule of logarithms, which states that ( \log(a) + \log(b) = \log(ab) ): [ \log((x+2)(x1)) = 1 ]

Rewrite the equation in exponential form. Remember that if ( \log_b(x) = y ), then ( b^y = x ): [ 10^1 = (x+2)(x1) ]

Simplify the equation: [ 10 = (x+2)(x1) ]

Expand and rearrange the equation: [ 10 = x^2 + x  2 ] [ x^2 + x  12 = 0 ]

Solve the quadratic equation. You can factorize or use the quadratic formula: [ x^2 + 4x  3x  12 = 0 ] [ x(x + 4)  3(x + 4) = 0 ] [ (x  3)(x + 4) = 0 ]
This gives two solutions: [ x  3 = 0 \rightarrow x = 3 ] [ x + 4 = 0 \rightarrow x = 4 ]
However, we need to check if these solutions satisfy the original equation. Since logarithms are only defined for positive numbers, we discard the solution ( x = 4 ).
Thus, the only solution to the equation ( \log(x+2) + \log(x1) = 1 ) is ( x = 3 ).
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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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