document.write( "Question 1206182: \(\log _{8}(x+2)-\log _{8}(x)=\log _{8}(30)\)
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Algebra.Com's Answer #843445 by Theo(13342)\"\" \"About 
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your problem statement is:
\n" ); document.write( "log8(x+2) - log8(x) = log8(30)
\n" ); document.write( "since log(a) - log(b) = log(a/b), you get:
\n" ); document.write( "log8((x+2)/x) = log8(30)
\n" ); document.write( "this is true if and only if (x+2)/x = 30
\n" ); document.write( "multiply both sides of that equation by x to get x+2 = 30x.
\n" ); document.write( "subtract x from both sides of that equati0on to get 2 = 29x.
\n" ); document.write( "solve for x to get x = 2/29.
\n" ); document.write( "that should be your answer.
\n" ); document.write( "to confirm, replace x with 2/29 in the original equation and solve.
\n" ); document.write( "log8(x+2) - log8(x) = log8(30) becomes log8(2/29 + 2) - log8(2/29) = log8(30).
\n" ); document.write( "by the log base conversion formula that says log8 = log/log(8), you get:
\n" ); document.write( "log(2/29 + 2)/log(8) - log(2/29)/log(8) = log(30)/log(8).
\n" ); document.write( "use your calculator to get 1.635630199 = 1.635630199, confirming the equation is true when x = 2/29.\r
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\n" ); document.write( "\n" ); document.write( "the log function on your calculator is log10 which translates to log to the base of 10.
\n" ); document.write( "the log base conversion formula says that log8(x) = log10(x)/log10(8).
\n" ); document.write( "since log10 is the log function on your calculator, this becomes log8(x) = log(x)/log(8).\r
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\n" ); document.write( "\n" ); document.write( "your solution is x = 2/29.\r
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