Log Maths Question

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purpleaki12
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#1
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#1
Hello just a small query on this AS level log question. Why do we only accept the negative answer but not the positive one? (Last line)


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mqb2766
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#2
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Have you tried testing the positive solution in the original equation?
When stuff is squared as part of algebraic manipulation, you need to be careful of introducing extranous solutions.
Last edited by mqb2766; 1 month ago
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purpleaki12
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#3
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(Original post by mqb2766)
Have you tried testing the positive solution in the original equation?
When stuff is squared as part of algebraic manipulation, you need to be careful of introducing extranous solutions.
Hi , thanks for the response , 4+4sqrt2 = 9.66 (a positive solution) whereas 4-4sqrt2= -1.66 ( a negative)
and the only answer allowed is the negative one. I don't understand why it can't be the positive solution , as I thought logs can't be negatives.
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mqb2766
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(Original post by purpleaki12)
Hi , thanks for the response , 4+4sqrt2 = 9.66 (a positive solution) whereas 4-4sqrt2= -1.66 ( a negative)
and the only answer allowed is the negative one. I don't understand why it can't be the positive solution , as I thought logs can't be negatives.
As per the previous post, have you tried subbing the "solutions" into the original equation to verify them?
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Ira Acedia
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#5
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(Original post by purpleaki12)
Hi , thanks for the response , 4+4sqrt2 = 9.66 (a positive solution) whereas 4-4sqrt2= -1.66 ( a negative)
and the only answer allowed is the negative one. I don't understand why it can't be the positive solution , as I thought logs can't be negatives.
You are correct, outside of Further Maths, logs can't be negative (as imaginary and complex numbers are completely ignored).

However, you aren't doing log(4-4(sqrt(2))), you're doing log(2-x) and log(x+5). So you have to make sure that both 2-x and x+5 are positive. The values you calculated at the end of you working are both values of x.

x+5 gives a positive value for both of them
2-x gives a positive value of 3.66 for the accepted answer, and -4.66 for the rejected answer.
Last edited by Ira Acedia; 1 month ago
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HardlyHuman
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(Original post by purpleaki12)
Hi , thanks for the response , 4+4sqrt2 = 9.66 (a positive solution) whereas 4-4sqrt2= -1.66 ( a negative)
and the only answer allowed is the negative one. I don't understand why it can't be the positive solution , as I thought logs can't be negatives.
1) as per the other posts, if you sub in x the 2 - x and x + 5 will no longer be negative
2) you can have negative logs, you will just need to introduce the imaginary plane
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mqb2766
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Seeing the answers been given, a good tip is to think about the domain of the equation before you start playing with algebraic manipulation as its sometimes easy to introduce extraneous solutions without realizing. For both logs to have a positive argument you must have
x < 2 and x > -5
That way you have simple inequalities to verify (or reject any extraneous) solutions
Last edited by mqb2766; 1 month ago
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