document.write( "Question 270469: Given that log 2 ≈ 0.301 and log 3 ≈ 0.477, find the following.\r
\n" ); document.write( "\n" ); document.write( "log6 27\r
\n" ); document.write( "\n" ); document.write( "Here is the work I have done, can someone check it for me?
\n" ); document.write( "log(6) = log(2*3)
\n" ); document.write( "log(2) log(3) = .301 .477 = .778
\n" ); document.write( "log6(27) = 1.84 \n" ); document.write( "
Algebra.Com's Answer #198395 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"log%286%2C+%2827%29%29\"
\n" ); document.write( "The key to this problem is to realize that a base 6 logarithm is hard to work with. We need to change the base to one that is easy to work with, like base 10 logarithms. Fortunately there is a formula for doing just this: \"log%28a%2C+%28x%29%29+=+log%28b%2C+%28x%29%29%2Flog%28b%2C+%28a%29%29\". Using this formula to change your base 6 logarithm to an expression of base 10 logarithms we get:
\n" ); document.write( "\"log%286%2C+%2827%29%29+=+log%28%2827%29%29%2Flog%28%286%29%29\"
\n" ); document.write( "We now have base 10 logarithms to work with. Next, since we are given log(2) and log(3), we want to express the arguments in terms of 2's and/or 3's. You already figured out how to express a 6 in terms of 2's and 3's. With a little thought I hope you see that \"27+=+3%5E3\". So rewriting the logarithms using 2's and 3's we get:
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\n" ); document.write( "Next we can use one property of logarithms, \"log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29\" to move the exponent of \"3%5E3\" out in front of the logarithm. And we can use another property of logarithms, \"log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28b%29%29\", to split the log(2*3) into separate logarithms:
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\n" ); document.write( "We have finally changed our original base 6 logarithm of 27 into an expression of base 10 logarithms of 2 and 3. We can now use the given values for log(2) and log(3) and simplify:
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\n" ); document.write( "Rounded to the nearest 1/100 this matches the answer you got. But I have no idea how you came up with this. The work you provided is grossly incomplete.
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