document.write( "Question 1148840: sqrt(125^x) = 5/(25^x) \n" ); document.write( "
Algebra.Com's Answer #770193 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
sqrt(125^x) = 5/(25^x)
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\"matrix%281%2C3%2C+sqrt%28125%5Ex%29%2C+%22=%22%2C+5%2F%2825%5Ex%29%29\"\r\n" );
document.write( "\"matrix%281%2C3%2C+%28sqrt%28125%5Ex%29%29%5E2%2C+%22=%22%2C+%285%2F25%5Ex%29%5E2%29\" --- Squaring both sides\r\n" );
document.write( "\"matrix%281%2C3%2C+125%5Ex%2C+%22=%22%2C+5%5E2%2F25%5E%282x%29%29\" \r\n" );
document.write( "\"matrix%281%2C3%2C+%285%5E3%29%5Ex%2C+%22=%22%2C+5%5E2%2F%285%5E2%29%5E%282x%29%29\" ------- Changing bases\r\n" );
document.write( "\"matrix%281%2C3%2C+5%5E%283x%29%2C+%22=%22%2C+5%5E2%2F5%5E%284x%29%29\" \r\n" );
document.write( "\"matrix%281%2C3%2C+5%5E%283x%29%2C+%22=%22%2C+5%5E%282+-+4x%29%29\" \r\n" );
document.write( "3x = 2 - 4x ------ Equating exponents, since their bases are equal\r\n" );
document.write( "3x + 4x = 2\r\n" );
document.write( "7x = 2\r\n" );
document.write( "\"highlight_green%28matrix%281%2C3%2C+x%2C+%22=%22%2C+2%2F7%29%29\"\r\n" );
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document.write( "FYI: LOGS are definitely NOT REQUIRED to solve this, as it's not that much of a COMPLEX exponents-problem.
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