You can put this solution on YOUR website! lnx+ln(x+2)=4
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One of the rules of logs says that if you add two logs, it is equivalent to taking the
logarithm of their product. Using this rule you can convert this problem to the following
form:
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ln(x*(x+2)) = 4
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Multiply out the terms in the parentheses and you get:
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ln(x^2 + 2x) = 4
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Now you can convert this to exponential form. Since the base of ln is e the exponential
form of this problem is:
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Calculator time. Find e^4. The answer to that is 54.59815003
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Substitute this value into the equation to get:
.
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Subtract 54.59815003 from both sides and transpose (switch sides) to get the standard
quadratic form:
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Solve using the quadratic formula. I'm assuming that if you are up to logarithms
you know how to use the quadratic formula. You will get two values for x ...
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x = 6.456416702 and x = -8.456416702
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The logarithm of a negative number has no meaning. (Enter -8.456416702 on your calculator
and see what happens when you try to take the natural log of that number.)
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So the only valid solution for this problem is x = 6.456416702
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check by plugging this value for x into the original equation:
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ln(x) + ln(x + 2)
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ln(6.456416702) + ln(6.456416702 + 2)
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ln(6.456416702) + ln(8.456416702)
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Calculator time again:
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1.865074474 + 2.134925526
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and if you add these two numbers together you do get 4 as the answer. This agrees
with the original equation in the problem. Therefore, the answer for x is good.
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Hope this helps.
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