SOLUTION: Agh...I am having major trouble understanding Logs! Please help?? 1. log x =3 (answers: a.30, b.300, c.1000, d.3000) 2. 9^x=11 (answers: a. 1.0192, b. 1.0913 , c. 1.131

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Agh...I am having major trouble understanding Logs! Please help?? 1. log x =3 (answers: a.30, b.300, c.1000, d.3000) 2. 9^x=11 (answers: a. 1.0192, b. 1.0913 , c. 1.131      Log On


   

Question 115400: Agh...I am having major trouble understanding Logs!
Please help??
1. log x =3 (answers: a.30, b.300, c.1000, d.3000)
2. 9^x=11 (answers: a. 1.0192, b. 1.0913 , c. 1.1314 , d. 1.1163)
thanks for any help!
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The first of these problems uses the following definition that relates the logarithmic form
to the exponential form:
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The logarithmic form log%28a%2CB%29=+y is equivalent to the exponential form a%5Ey+=+B
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Let's use this relationship on the problem. You are given:
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log%2810%2Cx+=+3%29
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Compare this to the logarithmic form above. If you do you will see that "a" in the logarithmic
form is 10 in your problem. Also you will see that y in the logarithmic form is 3 in your
problem. And B in the logarithmic form is x in your problem. Now all you have to do to convert
your problem is to go to the exponential form and plug in the corresponding values.
Start with the exponential form a%5Ey+=+B and substitute 10 for "a", 3 for y, and x for B.
When you do those substitutions you get as the exponential form of the given problem:
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10%5E3+=+x
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Cubing 10 results in 1000 and the exponential form reduces to just:
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1000+=+x
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That is the answer to the first problem ... x = 1000. This is answer c in your list of
answers.
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The second problem first involves taking the logarithm of both sides to get:
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log%2810%2C9%5Ex%29+=+log%2810%2C11%29
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On the left side you can use the logarithmic property that the log of a quantity that is raised
to an exponent is equal to the logarithm of the quantity multiplied by the exponent.
This means that log%2810%2C9%5Ex%29+=+x%2Alog%2810%2C9%29+. Substitute this into the equation and
you then have:
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x%2Alog%2810%2C9%29+=+log%2810%2C11%29
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Now you can use a calculator to find that:
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log%2810%2C9%29+=+0.954242509 and
log%2810%2C11%29+=+1.041392685
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Substitute these values into the equation and you have:
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x%2A0.954242509+=+1.041392685
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Solve for x by dividing both sides by 0.954242509 to get:
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x+=+1.041392685%2F0.954242509
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After you do the division on the right side ... using a calculator ... you have:
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x+=+1.09132917
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Answer b in your list of answers is the correct choice.
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Hope this helps you to understand logarithms a little bit more.
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