document.write( "Question 401308: use log12(3)=0.4421 and log12(7)=0.7831 to evaluate log12(48) \n" ); document.write( "
Algebra.Com's Answer #284059 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"log%2812%2C+%283%29%29+=+0.4421\"
\n" ); document.write( "\"log%2812%2C+%287%29%29+=+0.7831\"
\n" ); document.write( "We are given these two logarithms. Another base 12 logarithm we can use without having to be told is:
\n" ); document.write( "\"log%2812%2C+%2812%29%29+=+1\"

\n" ); document.write( "The \"trick\" to this kind of problem is to express the argument of the desired logarithm in terms of products, quotients and/or powers of the arguments of the known logarithms. In this problem the argument of the desired logarithm is 48. The arguments of the known logarithms are 3, 7 and 12. So we want to express 48 as some product(s), quotient(s) and/or power(s) of 3, 7 and/or 12.

\n" ); document.write( "First we can find that 48=12*4. But we don't know what \"log%2812%2C+%284%29%29\" is. Can we express a 4 in terms of 3, 7 and/or 12? Answer: 4 = 12/3. So now we have
\n" ); document.write( "\"48+=+12%2A%2812%2F3%29\"

\n" ); document.write( "Now we can find \"log%2812%2C+%2848%29%29\":
\n" ); document.write( "\"log%2812%2C+%2848%29%29+=+log%2812%2C+%2812%2A%2812%2F3%29%29%29\"
\n" ); document.write( "Now we can use a property of logarithms, \"log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29\", to split the logarithm of a product into the sum of the logarithms of the factors:
\n" ); document.write( "
\n" ); document.write( "Next we can use another property of logarithms, \"log%28a%2C+%28p%2Fq%29%29+=+log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29\", to split the logarithm of a quotient into the difference of the logarithms of the numerator and denominator:
\n" ); document.write( "
\n" ); document.write( "We can now replace each logarithm with its known value:
\n" ); document.write( "
\n" ); document.write( "And simplify:
\n" ); document.write( " \n" ); document.write( "
\n" );