document.write( "Question 1208680: Given that log 27+log base b 4=5 and log base a 27-log base a 4=1 without using tables find the values of a and b\r
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Algebra.Com's Answer #847076 by greenestamps(13198)\"\" \"About 
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\n" ); document.write( "When you want help with a problem, take the time to make sure you are making your post correctly.

\n" ); document.write( "Given that log \"red%28base%29\" \"red%28a%29\" 27+log base b 4=5 and log base a 27-log base \"red%28cross%28a%29%29\" \"red%28b%29\" 4=1

\n" ); document.write( "\"log%28a%2C27%29%2Blog%28b%2C4%29=5\"
\n" ); document.write( "\"log%28a%2C27%29-log%28b%2C4%29=1\"

\n" ); document.write( "Add the two equations:

\n" ); document.write( "\"2log%28a%2C27%29=6\"
\n" ); document.write( "\"log%28a%2C27%29=3\"
\n" ); document.write( "\"a%5E3=27\"
\n" ); document.write( "\"a=3\"

\n" ); document.write( "Substitute a=3 in either original equation:

\n" ); document.write( "\"log%283%2C27%29%2Blog%28b%2C4%29=5\"
\n" ); document.write( "\"3%2Blog%28b%2C4%29=5\"
\n" ); document.write( "\"log%28b%2C4%29=2\"
\n" ); document.write( "\"b%5E2=4\"
\n" ); document.write( "\"b=2\"

\n" ); document.write( "ANSWERS: a=3, b=2

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