document.write( "Question 165154: Express as a single logarithm with a coeffiecient of 1:\r
\n" ); document.write( "\n" ); document.write( "2*log(x)- 2*log(y)+4*log(z)\r
\n" ); document.write( "\n" ); document.write( "Many thanks for helping! \n" ); document.write( "
Algebra.Com's Answer #121737 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
you use two logarithmic relationships to get to this answer.
\n" ); document.write( "first relationship is log (a*b) = log(a) + log(b).
\n" ); document.write( "second relationship is log (a^b) = b*log(a).
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\n" ); document.write( "this is how it works in your equation.
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\n" ); document.write( "second relationship allows you to rewrite your equation as:
\n" ); document.write( "2*log(x) + 2*log(y) + 4*log(z) = log(x^2) + log(y^2) + log(z^4)
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\n" ); document.write( "first relationship allows you to rewrite your equation as:
\n" ); document.write( "log(x^2*y^2*z^4) ******************************************************
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\n" ); document.write( "that's your answer.
\n" ); document.write( "to prove it, let x, y, and z be any numbers chosen at random.
\n" ); document.write( "i chose:
\n" ); document.write( "x = 3
\n" ); document.write( "y = 7
\n" ); document.write( "z = 15
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\n" ); document.write( "2*log(3) + 2*log(7) + 4*log(15) = 7.348803626 ****************
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\n" ); document.write( "3^2 = 9
\n" ); document.write( "7^2 = 49
\n" ); document.write( "15^4 = 50625
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\n" ); document.write( "9*49*50625 = 22325625
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\n" ); document.write( "log(22325625) = 7.348803626 ******************
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\n" ); document.write( "answers match proving solution is correct.\r
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