document.write( "Question 616610: 2 logu125+8=14\r
\n" ); document.write( "\n" ); document.write( "The u is smaller than the g and is the base. I keep struggling with this problem and your help is greatly appreciated. Thank you \n" ); document.write( "
Algebra.Com's Answer #387790 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
you mean (log(125) to the base of u) + 8 = 14?
\n" ); document.write( "that would look like this:
\n" ); document.write( "log(u,125) = \"log%28u%2C125%29\"
\n" ); document.write( "from that, i gather that this problem is:
\n" ); document.write( "2*log(u,125) + 8 = 14 which would look like:
\n" ); document.write( "\"2%2Alog%28u%2C125%29+%2B+8+=+14\"
\n" ); document.write( "if that's what it is, then the solution would be as follows:
\n" ); document.write( "subtract 8 from both sides of the equation to get:
\n" ); document.write( "2*log(u,125) = 14 - 8 which becomes:
\n" ); document.write( "2*log(u,125) = 6
\n" ); document.write( "divide both sides of this equation by 2 to get:
\n" ); document.write( "log(u,125) = 3
\n" ); document.write( "by the laws of logarithms log(b,x) = y if and only if b^y = x
\n" ); document.write( "based on this, your problem then becomes:
\n" ); document.write( "log(u,125) = 3 if and only if u^3 = 125
\n" ); document.write( "take the cube root of both sides of this equation to get:
\n" ); document.write( "u = (125)^(1/3)
\n" ); document.write( "the cube root of 125 should be 5 because 5^3 = 125.
\n" ); document.write( "if you didn't know that, you would use your calculator to solve for u to get:
\n" ); document.write( "u = (125)^(1/3) = 5
\n" ); document.write( "to confirm this is correct, use that value of u to solve the original equation.
\n" ); document.write( "the original equation is:
\n" ); document.write( "2*log(u,125) + 8 = 14
\n" ); document.write( "since u = 5, this becomes:
\n" ); document.write( "2*log(5,125) + 8 = 14
\n" ); document.write( "you can use the log base conversion formula to make this equivalent to:
\n" ); document.write( "2*log(10,125)/log(10,5) + 8 = 14
\n" ); document.write( "since the LOG function of your calculator already solves for logs to the base of 10, your equation becomes:
\n" ); document.write( "2*LOG(125)/LOG(5) + 8 = 14
\n" ); document.write( "you can now use your calculator to solve this equation to get:
\n" ); document.write( "14 = 14 confirming that the value of 5 for u is good.
\n" ); document.write( "the log conversion formula is:
\n" ); document.write( "log(b,c) = log(d,c)/log(d,b)
\n" ); document.write( "what this says is that the log of c to the base of b is equal to:
\n" ); document.write( "the log of c to the base of d divided by the log of b to the base of d.
\n" ); document.write( "c is the original number that you want to get the log of.
\n" ); document.write( "b is the original base.
\n" ); document.write( "d is the new base.
\n" ); document.write( "you take the log of the same number to the base of d (the new base) and divide that by the log of b (the old base) to the base of d (the new base).
\n" ); document.write( "in solving a problem like this, you need to know the basic definition of logarithms that states:
\n" ); document.write( "log(b,x) = y if and only if b^y = x
\n" ); document.write( "in symbolic notation, this would look like this:
\n" ); document.write( "\"log%28b%2Cx%29+=+y\" if and only if \"b%5Ey+=+x\"
\n" ); document.write( "here's a reference that explains that in possibly a more elegant fashion than i could.
\n" ); document.write( "http://www.themathpage.com/aprecalc/logarithms.htm
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