Question 76241This question is from textbook algebra 2
: ln x+ln9x-20=1
This question is from textbook algebra 2
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! ln(x) + ln(9x) - 20 = 1
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Adding logarithms is the same as multiplying. So ln(x) + ln(9x) is the same as ln(x*9x)
and multiplying x*9x results in 9x^2. So now the equation is:
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ln(9x^2) - 20 = 1
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Now add 20 to both sides and you get:
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ln(9x^2) = 21
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by switching to the exponential form this can be transformed to:
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e^21 = 9x^2
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Divide both sides by 9 and transpose to get:
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x^2 = (e^21)/9
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Now use a calculator to find that e^21 = 1318815734 and then dividing that by 9 you get
146535081.6
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Substituting this for the right side of the equation results in:
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x^2 = 146535081.6
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Taking the square root of both sides results in x = 12105.16756
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Check this out by substituting this value for x into the original problem. You get:
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ln(12105.16756) + ln(9*12105.16756) - 20 = 1
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Using a calculator you will find that ln(12105.16756) = 9.401387711 and ln(9*12105.16756)
is ln(108946.508) and your calculator will convert this to 11.59861229. Substituting
this into the equation results in:
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9.401387711 + 11.59861229 - 20 = 1
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The sum of the first two terms is 21. Substituting 21 in place of the two terms gives:
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21 - 20 = 1
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This equation balances which tells us that x does equal 12105.16756
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Hope this helps you by providing one way to get a solution to this problem.
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