document.write( "Question 832425: Simplify.
\n" ); document.write( "Log4 ((sqrt(x^5*y^7))/z*w^4)\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #502044 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Hi, there--\r\n" );
document.write( "\r\n" );
document.write( "THE PROBLEM:\r\n" );
document.write( "Simplify:\r\n" );
document.write( "\"log%284%2C%28%28sqrt%28x%5E5%2Ay%5E7%29%29%2Fz%2Aw%5E4%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "A SOLUTION:\r\n" );
document.write( "We work from the outside in, using the log laws.\r\n" );
document.write( "\r\n" );
document.write( "Apply the Log Law for Division-to-Subtraction: log(a/b) = log(a) - log(b)\r\n" );
document.write( "\"log%284%2C%28%28sqrt%28x%5E5%2Ay%5E7%29%29%2Aw%5E4%29%29-log%284%2Cz%29\"\r\n" );
document.write( "\r\n" );
document.write( "Apply the Log Law for Multiplication-to-Addition: log(ab) = log(a) + log(b)\r\n" );
document.write( "\"log%284%2C%28sqrt%28x%5E5%2Ay%5E7%29%29%29-log%284%2C%28z%29%29%2Blog%284%2C%28w%5E4%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Now, we are ready to deal with the square root. Recall that take the square root of a number is equivalent \r\n" );
document.write( "to raising that number to the 1/2=0.5 power.\r\n" );
document.write( "\"log%284%2C%28%28x%5E5%2Ay%5E7%29%5E0.5%29%29-log%284%2C%28z%29%29%2Blog%284%2C%28w%5E4%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Apply the Power Rule for Logarithms: log(a^n) = n * log(a)\r\n" );
document.write( "\"0.5%2Alog%284%2C%28x%5E5%2Ay%5E7%29%29-log%284%2C%28z%29%29%2B4%2Alog%284%2C%28w%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Apply the Log Law for Multiplication-to-Addition again.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Apply the power rule again.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Distribute the 0.5 to clear some parentheses.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Good luck with your math,\r\n" );
document.write( "\r\n" );
document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
document.write( "
\n" ); document.write( "
\n" );