document.write( "Question 1148840: sqrt(125^x) = 5/(25^x) \n" ); document.write( "
Algebra.Com's Answer #770173 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
start with:
\n" ); document.write( "sqrt(125^x) = 5/(25^x)
\n" ); document.write( "rewrite it as:
\n" ); document.write( "(125^x)^(1/2) = 5/(25^x)
\n" ); document.write( "simplify that to:
\n" ); document.write( "125^(x/2) = 5/(25^x)
\n" ); document.write( "multiply both sides of that equation by 25^x to get:
\n" ); document.write( "125^(x/2) * 25^x = 5
\n" ); document.write( "take the log of both sides of this equation to get:
\n" ); document.write( "log(125^(x/2) * 25^x) = log(5)
\n" ); document.write( "use log rules to translate that to:
\n" ); document.write( "log(125^(x/2)) + log(25^x) = log(5)
\n" ); document.write( "simplify that to:
\n" ); document.write( "x/2 * log(125) + x * log(25) = log(5)
\n" ); document.write( "factor out the x to get:
\n" ); document.write( "x * (1/2 * log(125) + log(25)) = log(5)
\n" ); document.write( "divide both sides of that equation by (1/2 * log(125) + log(25)) to get:
\n" ); document.write( "x = log(5) / (1/2 * log(125) + log(25))
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = .2857142857
\n" ); document.write( "replace x in the original equation to get:
\n" ); document.write( "sqrt(125^x) = 5/(25^x) becomes sqrt(125^.2857142857) = 5 / 25^.2857142857 which becomes 1.993235316 = 1.993235316 which is true.\r
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\n" ); document.write( "\n" ); document.write( "your solution is that the value for x is .2857142857\r
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\n" ); document.write( "\n" ); document.write( "the properties of logs that were used are:\r
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\n" ); document.write( "\n" ); document.write( "log(a * b) = log(a) + log(b) and log(a^x) = x*log(a)\r
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