document.write( "Question 554033: If log x^5y^3=25 and log x/y=3 what is log x? \n" ); document.write( "
Algebra.Com's Answer #361178 by Theo(13342)\"\" \"About 
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if log(x^5y^3) = 25, this means that:
\n" ); document.write( "10^25 = x^5y^3
\n" ); document.write( "if log(x/y) = 3, this means that:
\n" ); document.write( "10^3 = x/y
\n" ); document.write( "we can solve for x in this equation to get:
\n" ); document.write( "x = 10^3y
\n" ); document.write( "we can substitute in the equation of:
\n" ); document.write( "10^25 = x^5y^3 to get:
\n" ); document.write( "10^25 = (10^3y)^5*y^3
\n" ); document.write( "this becomes:
\n" ); document.write( "10^25 = 10^15y^5*y^3
\n" ); document.write( "we simplify this to get:
\n" ); document.write( "10^25 = 10^15*y^8
\n" ); document.write( "we divide both sides of this equation by 10^15 to get:
\n" ); document.write( "10^25/10^15 =y^8
\n" ); document.write( "we simplify to get:
\n" ); document.write( "10^10 = y^8
\n" ); document.write( "we take the 8th root of both sides of this equation to get:
\n" ); document.write( "10^(10/8) = y which simplifies to:
\n" ); document.write( "10^(1.25 = y which leads to:
\n" ); document.write( "y = 17.78279410
\n" ); document.write( "since x = 10^3y which is the same as 1000y, this means that:
\n" ); document.write( "x = 17782.79410
\n" ); document.write( "y = 17.7829410
\n" ); document.write( "with those values for x and y, we get:
\n" ); document.write( "first equation:
\n" ); document.write( "log(x^5*y^3) = log(17782.79410^5*17.7829410^3) = log(10^25) = 25
\n" ); document.write( "second equation:
\n" ); document.write( "log(x/y) = log(17782.794/17.7829410) = log(1000) = 3
\n" ); document.write( "all the numbers check out.
\n" ); document.write( "the values for x and y are good.
\n" ); document.write( "x = 17782.79410
\n" ); document.write( "y = 17.7829410
\n" ); document.write( "log(x) = log(17782.79410) = 4.25
\n" ); document.write( "log(y) = log(17.7829410) = 1.25
\n" ); document.write( "your answer to the question is:
\n" ); document.write( "log(x) = 4.25\r
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