document.write( "Question 115400: Agh...I am having major trouble understanding Logs!\r
\n" ); document.write( "\n" ); document.write( "Please help??\r
\n" ); document.write( "\n" ); document.write( "1. log x =3 (answers: a.30, b.300, c.1000, d.3000)\r
\n" ); document.write( "\n" ); document.write( "2. 9^x=11 (answers: a. 1.0192, b. 1.0913 , c. 1.1314 , d. 1.1163)\r
\n" ); document.write( "\n" ); document.write( "thanks for any help! \n" ); document.write( "
Algebra.Com's Answer #84031 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
The first of these problems uses the following definition that relates the logarithmic form
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\n" ); document.write( "The logarithmic form \"log%28a%2CB%29=+y\" is equivalent to the exponential form \"a%5Ey+=+B\"
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\n" ); document.write( "Let's use this relationship on the problem. You are given:
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\n" ); document.write( "\"log%2810%2Cx+=+3%29\"
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\n" ); document.write( "Compare this to the logarithmic form above. If you do you will see that \"a\" in the logarithmic
\n" ); document.write( "form is 10 in your problem. Also you will see that y in the logarithmic form is 3 in your
\n" ); document.write( "problem. And B in the logarithmic form is x in your problem. Now all you have to do to convert
\n" ); document.write( "your problem is to go to the exponential form and plug in the corresponding values.
\n" ); document.write( "Start with the exponential form \"a%5Ey+=+B\" and substitute 10 for \"a\", 3 for y, and x for B.
\n" ); document.write( "When you do those substitutions you get as the exponential form of the given problem:
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\n" ); document.write( "\"10%5E3+=+x\"
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\n" ); document.write( "Cubing 10 results in 1000 and the exponential form reduces to just:
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\n" ); document.write( "\"1000+=+x\"
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\n" ); document.write( "That is the answer to the first problem ... x = 1000. This is answer c in your list of
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\n" ); document.write( "The second problem first involves taking the logarithm of both sides to get:
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\n" ); document.write( "\"log%2810%2C9%5Ex%29+=+log%2810%2C11%29\"
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\n" ); document.write( "On the left side you can use the logarithmic property that the log of a quantity that is raised
\n" ); document.write( "to an exponent is equal to the logarithm of the quantity multiplied by the exponent.
\n" ); document.write( "This means that \"log%2810%2C9%5Ex%29+=+x%2Alog%2810%2C9%29+\". Substitute this into the equation and
\n" ); document.write( "you then have:
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\n" ); document.write( "\"x%2Alog%2810%2C9%29+=+log%2810%2C11%29\"
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\n" ); document.write( "Now you can use a calculator to find that:
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\n" ); document.write( "\"log%2810%2C9%29+=+0.954242509\" and
\n" ); document.write( "\"log%2810%2C11%29+=+1.041392685\"
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\n" ); document.write( "Substitute these values into the equation and you have:
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\n" ); document.write( "\"x%2A0.954242509+=+1.041392685\"
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\n" ); document.write( "Solve for x by dividing both sides by 0.954242509 to get:
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\n" ); document.write( "\"x+=+1.041392685%2F0.954242509\"
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\n" ); document.write( "After you do the division on the right side ... using a calculator ... you have:
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\n" ); document.write( "\"x+=+1.09132917\"
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\n" ); document.write( "Answer b in your list of answers is the correct choice.
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\n" ); document.write( "Hope this helps you to understand logarithms a little bit more.
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