SOLUTION: lnx^lnx=4 for x?

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Question 524227: lnx^lnx=4 for x?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given to solve:
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ln%28x%5Eln%28x%29%29+=+4
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By the rules of logarithms the exponent can be brought out as a multiplier of the logarithm. When you do that, the result is:
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ln%28x%29%2Aln%28x%29+=+4
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But the left side then becomes:
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%28ln%28x%29%29%5E2+=+4
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And the right side can be written as shown below:
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%28ln%28x%29%29%5E2+=+4%5E2
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In this case, the square root of 4 can either be +2 or -2. Therefore, taking the square root of both sides then results in either:
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ln%28x%29+=+2 or ln%28x%29+=+-2
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These can then be converted to the exponential form by raising the base of natural logarithm, which is e, to the powers on the right side and this will equal x. In other words:
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x+=+e%5E2 or x+=+e%5E%28-2%29
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Hope this helps you to understand logarithms a little better.