document.write( "Question 1139360: log3 x = m can you please tell how solve this question?? \n" ); document.write( "
Algebra.Com's Answer #759813 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
log3(x) = m if and only if x = 3^m.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "your solution would be x = 3^m.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "if so, then log3(3^m) = m would have to be true.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "you should be able to take any value of m and show that this is true.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "for example, log3(3^5) should be equal to 5.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "since log3(3^5) is equal to 5 * log3(3) and since log3(3) = 1, then you get 5 = 5, which is true.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "another way to confirm is to use the log base conversion formula and solve using your calculator.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the log base conversion formula says that logb(x) = logc(x) / logc(b).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "if b is equal to 3 and c is equal to 10, this becomes log3(x) = log10(x) / log10(3).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "since log10 is the log function of your calculator, then you get log3(x) = log(x)/log(3).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "when x = 3^5, this becomes log3(3^5) = log(3^5) / log(3).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "you use your calculator to get log(3^5) / log(3) = 5.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "you can also see thqt log3(3^5)) = log(3^5) / log(3), and swince log(3^5) is equal to 5 * log(3), this becomes log3(3^5) = 5 * log(3) / log(3) which is equal to 5 * 1 which is equal to 5.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "i'm not exactly sure what else you can do with this.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the basic property of logs says that logb(x) = y if and only if x = b^y.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "when b = 3 and y = m, this becomes log3(x) = m if and only if x = 3^m.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "that's what we started with above.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "some basic properties of logs are:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "logb(x) = logc(x) / logc(b)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "we used this one above.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "log(x^a) = a * log(x)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "we used this one above.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "logb(b) = 1.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "i think we used this one above as well.
\n" ); document.write( "you can confirm this one for base of 10 using the log function of your calculator, i.e. log(10) will be equal to 1.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );