document.write( "Question 253873: If a=log base 10 of 2, and b= log base 10 of 3. Express log base 81 of 80 in terms of a & b without incorporating the word \"log\" in your expression. \n" ); document.write( "

Algebra.Com's Answer #186238 by drk(1908) $\"\"$ $\"About$

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We have the following:
\n" ); document.write( "(i) $\"log_81%2880%29\"$
\n" ); document.write( "By change of base, we get
\n" ); document.write( "(ii) $\"log%2880%29%2Flog%2881%29\"$
\n" ); document.write( "(iii) $\"Log%2880%29+=+log%288%2A10%29+=+log%282%5E3%2A10%29+=+3log%282%29+%2B+1\"$
\n" ); document.write( "(iv) $\"log%2881%29+=+log%283%5E4%29\"$ = $\"log%283%5E4%29+=+4log%283%29\"$
\n" ); document.write( "substituting (iii) and (iv) into (ii) we get
\n" ); document.write( "(v) $\"%283log%282%29+%2B+1%29%2F%284log%283%29%29\"$
\n" ); document.write( " We were given
\n" ); document.write( "a=log_10(2), and b= log_10(3).
\n" ); document.write( "Substituting, we get
\n" ); document.write( " $\"%283a+%2B+1%29%2F%284b%29\"$ \n" ); document.write( "

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