document.write( "Question 1129970: Find the exact value of e^LOGe^2 16\r
\n" ); document.write( "\n" ); document.write( "The answer is 4, but I am unsure as to why.\r
\n" ); document.write( "\n" ); document.write( "If possible, please show multiple methods (with step by step breakdown). Here is what I've gathered so far:\r
\n" ); document.write( "\n" ); document.write( "Method 1:
\n" ); document.write( "1. e^LOGe^2 2^4
\n" ); document.write( "2. e^(4/2)LOGe 2 ( I don't understand where the 4 divided by 2 comes into play, and which property dictates it )
\n" ); document.write( "3. e^2LOGe 2
\n" ); document.write( "4. e^LOGe 4 (Where did the 4 come from? Did both of the 2's get multiplied?)
\n" ); document.write( "5. =4\r
\n" ); document.write( "\n" ); document.write( "Method 2:
\n" ); document.write( "1. e^LOGe^2 16
\n" ); document.write( "2. e^(1/2)LN 16 (Where did the 1/2 come from?)
\n" ); document.write( "3. sqrt(e^LN 16) (Why is the entire expression inside the square root?)
\n" ); document.write( "4. sqrt(16) (Why did the \"e^LN\" portion inside the square root disappear?)
\n" ); document.write( "5. =4\r
\n" ); document.write( "\n" ); document.write( "Is it also possible to solve this problem by using the base change method?\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance. \n" ); document.write( "

Algebra.Com's Answer #853664 by MathTherapy(10699) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Find the exact value of e^LOGe^2 16\r\n" );
document.write( "\r\n" );
document.write( "The answer is 4, but I am unsure as to why.\r\n" );
document.write( "\r\n" );
document.write( "If possible, please show multiple methods (with step by step breakdown). Here is what I've gathered so far:\r\n" );
document.write( "\r\n" );
document.write( "Method 1:\r\n" );
document.write( "1. e^LOGe^2 2^4\r\n" );
document.write( "2. e^(4/2)LOGe 2 ( I don't understand where the 4 divided by 2 comes into play, and which property dictates it )\r\n" );
document.write( "3. e^2LOGe 2\r\n" );
document.write( "4. e^LOGe 4 (Where did the 4 come from? Did both of the 2's get multiplied?)\r\n" );
document.write( "5. =4\r\n" );
document.write( "\r\n" );
document.write( "Method 2:\r\n" );
document.write( "1. e^LOGe^2 16\r\n" );
document.write( "2. e^(1/2)LN 16 (Where did the 1/2 come from?)\r\n" );
document.write( "3. sqrt(e^LN 16) (Why is the entire expression inside the square root?)\r\n" );
document.write( "4. sqrt(16) (Why did the \"e^LN\" portion inside the square root disappear?)\r\n" );
document.write( "5. =4\r\n" );
document.write( "\r\n" );
document.write( "Is it also possible to solve this problem by using the base change method?\r\n" );
document.write( "\r\n" );
document.write( "Thanks in advance.\r\n" );
document.write( "==================\r\n" );
document.write( "Find the exact value of e^LOGe^2 16 ===> \r\n" );
document.write( "             Let \r\n" );
document.write( "              ---- Converting to EXPONENTIAL form\r\n" );
document.write( "             \r\n" );
document.write( "                 ----- Exponents are equal. and so are the bases\r\n" );
document.write( "                 \r\n" );
document.write( "         ---- Back-substituting  for t\r\n" );
document.write( "\r\n" );
document.write( "APPLYING ,  now becomes: , which is SIMPLY 4\r\n" );
document.write( "OR\r\n" );
document.write( "Find the exact value of e^LOGe^2 16 ===> \r\n" );
document.write( "First of all, let's EXTRACT the exponent,  from the expression.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "APPLYING ,  now becomes: , which is SIMPLY 4.

\n" ); document.write( "

\n" );