document.write( "Question 1148535: If a and b are positive numbers such that a^b=b^a and b=9a, then what is the value of a? \n" ); document.write( "

Algebra.Com's Answer #769878 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "If   =   and  b = 9a,  then\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "     = ;\r\n" );
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document.write( "        then, since indexes on the left and on the right are equal, the bases    and    must be equal too,  which gives\r\n" );
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document.write( "     = 9a.\r\n" );
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document.write( "It gives\r\n" );
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document.write( "     = 9.\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    a =  = .    ANSWER\r\n" );
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