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How do I solve this: lg (1-x) + lg (1+x) = lg0,75?
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<blockquote data-quote="gAytheist" data-source="post: 2727911" data-attributes="member: 913248"><p>Sorry, but you are way off.</p><p></p><p>First, log(1-x) ? log(1) - log(x)</p><p></p><p>Remember this rule:</p><p>log(a*b) = log(a) + log(b)</p><p></p><p>You have </p><p>log(1-x) + log(1+x) = log(c) where c is a constant [equal to 0,75 in this particular case]</p><p></p><p>Using the rule I mentioned above you can write the left hand side as:</p><p>log[(1-x)(1+x)] = log(c)</p><p>expand what's in the square brackets to get:</p><p>log(1 - x^2) = log(c)</p><p></p><p>Now you have log's on both sides and if they are to be equal then their arguments have to be equal. This means</p><p>(1 - x^2) = c</p><p></p><p>Rewrite this as:</p><p>x^2 - 1 + c = 0</p><p>substitute 0,75 for c to get</p><p>x^2 - 0,25 = 0</p><p></p><p>You should recognize the form on the left as something you can easily factor.</p><p>(x - 0,5)(x + 0,5) = 0</p><p></p><p>so x = ± 0,5</p></blockquote><p></p>
[QUOTE="gAytheist, post: 2727911, member: 913248"] Sorry, but you are way off. First, log(1-x) ? log(1) - log(x) Remember this rule: log(a*b) = log(a) + log(b) You have log(1-x) + log(1+x) = log(c) where c is a constant [equal to 0,75 in this particular case] Using the rule I mentioned above you can write the left hand side as: log[(1-x)(1+x)] = log(c) expand what's in the square brackets to get: log(1 - x^2) = log(c) Now you have log's on both sides and if they are to be equal then their arguments have to be equal. This means (1 - x^2) = c Rewrite this as: x^2 - 1 + c = 0 substitute 0,75 for c to get x^2 - 0,25 = 0 You should recognize the form on the left as something you can easily factor. (x - 0,5)(x + 0,5) = 0 so x = ± 0,5 [/QUOTE]
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