document.write( "Question 596154: what is the decimal approximation of log7 988
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Algebra.Com's Answer #377574 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find a decimal approximation for a logarithm it must be a logarithm of a base your calculator \"knows\": base 10 (common) or base r (natural, ln).

\n" ); document.write( "So to find a base 7 logarithm you must use the change of base formula to convert it from a base 7 log into base 10 or base e logs. The change of base formula is:
\n" ); document.write( " $\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"$
\n" ); document.write( "(Note that the formula converts a log of one base into two logs of another base.)

\n" ); document.write( "I'm going to convert the base 7 log into base e logs:
\n" ); document.write( " $\"log%287%2C+%28988%29%29+=+ln%28988%29%2Fln%287%29\"$

\n" ); document.write( "Now just get out your calculator (or computer calculator program) and find the two logs and then divide them. (Important: Do NOT divide 988 and 7 and then find the log. It doesn't work right that way.)

\n" ); document.write( "And finally, if we had converted the base 7 log to base 10 logs instead, we would still get the same answer! \n" ); document.write( "

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