document.write( "Question 770252: Please help me solve this: Express the following as a single logarithm.\r
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Algebra.Com's Answer #469390 by ramkikk66(644) $\"\"$ $\"About$

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document.write( "2log(a)1/2 + 3log(a)4 - log(a)4/5\r\n" );
document.write( "Remember that\r\n" );
document.write( "log x + log y = log (x*y)\r\n" );
document.write( "log x - log y = log (x/y)\r\n" );
document.write( "n * log x = log (x^n)\r\n" );
document.write( "Take each part of the given expression and simplify. \r\n" );
document.write( "2*log(a)(1/2) = log(a)((1/2)^2) = log(a)(1/4)\r\n" );
document.write( "3*log(a)(4) = log(a)(4^3) = log(a)(64)\r\n" );
document.write( "So 2log(a)1/2 + 3log(a)4 = log(a)(1/4) + log(a)(64) = log(a) ((1/4)*64))\r\n" );
document.write( "= log(a)(16)\r\n" );
document.write( "So the expression is\r\n" );
document.write( "log (a)(16) - log(a)(4/5)\r\n" );
document.write( "= log(a)(16/(4/5)) = log(a)(16*5/4) = log(a)(20)\r\n" );
document.write( "Single logarithm is log(a)(20) i.e. log 20 to the base a.\r\n" );
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