document.write( "Question 400998: Please show how to condense the following expressions:
\n" ); document.write( "2 log 9 + 5 log x + log 1/3
\n" ); document.write( "3 ln x + ln y + ln 10
\n" ); document.write( "2(ln2 - ln x) + (ln x - ln4) \n" ); document.write( "
Algebra.Com's Answer #283777 by lwsshak3(11628)\"\" \"About 
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Please show how to condense the following expressions:
\n" ); document.write( "2 log 9 + 5 log x + log 1/3
\n" ); document.write( "3 ln x + ln y + ln 10
\n" ); document.write( "2(ln2 - ln x) + (ln x - ln4)
\n" ); document.write( "rules to remember:
\n" ); document.write( "when multiplying numbers, add their logarithms
\n" ); document.write( "when dividing numbers, subtract their logarithms
\n" ); document.write( "for numbers with exponents, multiply exponent times logarithm of the number
\n" ); document.write( "first expression
\n" ); document.write( "2 log 9 + 5 log x + log 1/3
\n" ); document.write( "=log9^2+logx^5+log1-log3 (log 1 of any base=0)
\n" ); document.write( "=log9^2+logx^5-log3
\n" ); document.write( "=log((9^2)*(x^5)/3)
\n" ); document.write( "=log((81)*(x^5)/3)
\n" ); document.write( "=log(27*x^5)
\n" ); document.write( "second expression
\n" ); document.write( "3 ln x + ln y + ln 10
\n" ); document.write( "=lnx^3+lny+ln10
\n" ); document.write( "=ln(x^3*y*10)
\n" ); document.write( "third expression
\n" ); document.write( "2(ln2 - ln x) + (ln x - ln4)
\n" ); document.write( "=2ln2-2lnx+lnx-ln4
\n" ); document.write( "=2ln2-lnx-ln4
\n" ); document.write( "=2ln2-(lnx+ln4)
\n" ); document.write( "=ln(2^2/4x)
\n" ); document.write( "=ln(4/4x)
\n" ); document.write( "=ln(1/x)\r
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