document.write( "Question 957905: use the change of base formula to evaluate log6 12. then convert log6 12 to a logarithm in base 3. round to the nearest thousandth \n" ); document.write( "

Algebra.Com's Answer #585459 by jsmallt9(3758) $\"\"$ $\"About$

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Since 12 is not a well-known power of 6, we will need to use a calculator to evaluate $\"log%286%2C+%2812%29%29\"$ . Since most calculators do not have a button for base 6 logs we will need to use the change of base formula to convert to logarithms of a base our calcuator does have. If calculators have any buttons for logarithms at all they have buttons for base 10 and/or base e (\"log\" and/or \"ln\"). So we will convert $\"log%286%2C+%2812%29%29\"$ to one of these bases.

\n" ); document.write( "The change of base formula is $\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+a%29%29\"$ . We can use this to change a base 6 log to base 10:
\n" ); document.write( " $\"log%286%2C+%2812%29%29+=+log%28%2812%29%29%2Flog%28%286%29%29\"$
\n" ); document.write( "... or to base e logs:
\n" ); document.write( " $\"log%286%2C+%2812%29%29+=+ln%2812%29%2Fln%286%29\"$

\n" ); document.write( "I will leave it up to you and your calculator to find the decimal value. (Just be sure to find the two logs first, then divide them.) The answer is the same whether you use log or ln. (Try it and see!)

\n" ); document.write( "To change $\"log%286%2C+%2812%29%29\"$ into base 3 logs:
\n" ); document.write( " $\"log%286%2C+%2812%29%29+=+log%283%2C+%2812%29%29%2Flog%283%2C+%286%29%29\"$ \n" ); document.write( "

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