document.write( "Question 1122163: given that log8^(p+2) +log8^q=r-1/3and log2^(p-2)-log2^q=2r+1 then show that pē=4+32^r \n" ); document.write( "
Algebra.Com's Answer #738441 by greenestamps(13203)\"\" \"About 
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\n" ); document.write( "The \"^\" symbol is used to represent exponents -- not to indicate the base of a logarithm. Your question is

\n" ); document.write( "Given that \"log%288%2C%28p%2B2%29%29%2Blog%288%2C%28q%29%29=r-1%2F3\" and \"log%282%2C%28p-2%29%29-log%282%2C%28q%29%29=2r%2B1\" then show that \"p%5E2+=+4%2B32%5Er\"

\n" ); document.write( "It looks ugly (especially the way you showed it!), but everything falls in place nicely using basic rules of logarithms. Specifically, we need to use

\n" ); document.write( "log(a)+log(b) = log(ab)
\n" ); document.write( "log(a)-log(b) = log(a/b)
\n" ); document.write( "log base 2 of x = 3*log base 8 of x, since 8 = 2^3

\n" ); document.write( "(1) \"log%288%2C%28p%2B2%29%29%2Blog%288%2C%28q%29%29=r-1%2F3\" Given

\n" ); document.write( "(2) \"log%282%2C%28p-2%29%29-log%282%2C%28q%29%29=2r%2B1\" Given

\n" ); document.write( "(3) \"log%288%2C%28q%28p%2B2%29%29%29=r-1%2F3\" from (1)

\n" ); document.write( "(4) \"log%282%2C%28q%28p%2B2%29%29%29+=+3r-1\" from (3)

\n" ); document.write( "(5) \"log%282%2C%28%28p-2%29%2Fq%29%29+=+2r%2B1\" from (2)

\n" ); document.write( "(6) \"log%282%2C%28p%5E2-4%29%29+=+5r\" from (4) and (5)

\n" ); document.write( "(7) \"p%5E2-4+=+2%5E%285r%29+=+32%5Er\" (definition of log base 2)
\n" ); document.write( "(8) \"p%5E2+=+4%2B32%5Er\" \n" ); document.write( "
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