document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039520>Question 1039520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given that , 10^0.48 = x,10^0.70 =y and x^z =y^2, then the value of z is\r<BR>\n" );
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document.write( "a)1.45<BR>\n" );
document.write( "b)1.88<BR>\n" );
document.write( "c)2.9<BR>\n" );
document.write( "d)3.7<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654278 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given that:\r<BR>\n" );
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document.write( "x = 10^(.48)<BR>\n" );
document.write( "y = 10^(.7)<BR>\n" );
document.write( "x^z = y^2.\r<BR>\n" );
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document.write( "replace x with 10^(.48) and replace y with 10^(.7) and you get:<BR>\n" );
document.write( "(10^(.48))^z = (10^(.7))^2\r<BR>\n" );
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document.write( "since (a^b)^c = a^(b*c), you get:\r<BR>\n" );
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document.write( "(10^(.48))^z = (10^(.7))^2 becomes 10^(.48*z) = 10^(.7*2)<BR>\n" );
document.write( "simplify this to get 10^(.48*z) = 10^(1.4)\r<BR>\n" );
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document.write( "this is true if and only if .48*z = 1.4.<BR>\n" );
document.write( "solve for z to get z = 1.4/.48 = 2.91666666667<BR>\n" );
document.write( "this rounds to z = 2.9\r<BR>\n" );
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document.write( "that would be selection c.\r<BR>\n" );
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document.write( "you would confirm by replacing z with 2.91666666667 in the original equation to get:\r<BR>\n" );
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document.write( "(10^.48)^(2.91666666667) = 25.11886432<BR>\n" );
document.write( "(10^.7)^2 = 25.11886436\r<BR>\n" );
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document.write( "they're the same, so the the solution is correct.\r<BR>\n" );
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document.write( "z = 2.9 rounded to the nearest tenth.\r<BR>\n" );
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