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You can put this solution on YOUR website!
original equation to be solved is:
\n" ); document.write( "9*log(5,x) = 25*log(x,5)
\n" ); document.write( "log(5,x) means log of x to the base of 5.
\n" ); document.write( "log(x,5) means log of 5 to the base of x.
\n" ); document.write( "convert everything to base of 5 using the base conversion formula of log(b,x) = log(c,x)/log(c,b).
\n" ); document.write( "original equation of 9*log(5,x) = 25*log(x,5) becomes:
\n" ); document.write( "9*log(5,x) = 25*log(5,5)/log(5,x)
\n" ); document.write( "since log(5,5) is equal to 1, this equation becomes:
\n" ); document.write( "9*log(5,x) = 25/log(5,x)
\n" ); document.write( "multiply both sides of this equation by log(5,x) and divide both sides of this equation by 9 to get:
\n" ); document.write( "log(5,x) * log(5,x) = 25/9
\n" ); document.write( "this can be written as:
\n" ); document.write( "(log(5,x))^2 = 25/9
\n" ); document.write( "take the square root of both sides of this equation to get:
\n" ); document.write( "log(5,x) = +/- sqrt(25/9) which becomes:
\n" ); document.write( "log(5,x) = +/- 5/3
\n" ); document.write( "your possible answers are:
\n" ); document.write( "log(5,x) = 5/3
\n" ); document.write( "log(5,x) = -5/3
\n" ); document.write( "from the basic definition of logarithms, you get:
\n" ); document.write( "log(b,x) = c if and only if b^c = x
\n" ); document.write( "apply this to your first possible answer and you get:
\n" ); document.write( "log(5,x) = 5/3 if and only if 5^(5/3) = x
\n" ); document.write( "that's one of your possible answers.
\n" ); document.write( "x = 5^(5/3)
\n" ); document.write( "apply this to your second possible answer and you get:
\n" ); document.write( "log(5,x) = -5/3 if and only if 5^(-5/3) = x
\n" ); document.write( "that's the other of your possible answers.
\n" ); document.write( "5^(5/3) resolves to 14.62008869
\n" ); document.write( "5^-(5/3) resolves to 1/5^(5/3) which resolves to .068399038
\n" ); document.write( "to see if these answers are good, you need to substitute them into your original equation by substituting them in place of x.
\n" ); document.write( "before you do that, however, you need to convert equation to base of 10 so you can solve it using your calculator.
\n" ); document.write( "your original equation of:
\n" ); document.write( "9*log(5,x) = 25*log(x,5) becomes:
\n" ); document.write( "9*LOG(x)/LOG(5) = 25*LOG(5)/LOG(x)
\n" ); document.write( "all you need to do now is substitute.
\n" ); document.write( "when x = 14.62008869, your formula becomes:
\n" ); document.write( "9*LOG(14.6200869)/LOG(5) = 25*LOG(5)/LOG(14.6200869)
\n" ); document.write( "solve this using your calculator and you get:
\n" ); document.write( "15 = 15, so x = 14.62008869 is good.
\n" ); document.write( "remember 14.62008869 is equivalent to 5^(5/3)
\n" ); document.write( "when x = .068399038, your formula becomes:
\n" ); document.write( "9*LOG(.068399038)/LOG(5) = 25*LOG(5)/LOG(.068399038)
\n" ); document.write( "solve this using your calculator and you get:
\n" ); document.write( "-15 = -15
\n" ); document.write( "remember .068399038 is equivalent to 5^-(5/3) which is equialent to 1/5^(5/3)
\n" ); document.write( "both answers are good.
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