document.write( "Question 283777: how do u simplify log7 7^5 \n" ); document.write( "

Algebra.Com's Answer #205971 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%287%2C+%287%5E5%29%29\"$
\n" ); document.write( "If you understand what logarithms are, you can see what the answer is. In general, $\"log%28a%2C+%28b%29%29\"$ represents the exponent for \"a\" that results in \"b\". Your specific logarithm represents the exponent for 7 that results in $\"7%5E5\"$ . And what exponent do you put on 7 to get $\"7%5E5\"$ ? Answer: 5, of course!.

\n" ); document.write( "Another way to figure this out is to use the property of logarithms,

\n" ); document.write( "Since $\"log%287%2C+%287%29%29+=+1\"$ by definition, this simplifies to 5.

\n" ); document.write( "A last resort way to do this is to use the base conversion formula, $\"log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29\"$ , to convert your logarithm into one your calculator \"knows\". Using this formula to convert your base 7 logarithm into an expression of base 10 logarithms we get
\n" ); document.write( " $\"log%28%287%5E5%29%29%2Flog%28%287%29%29\"$
\n" ); document.write( "Now you can use your calculator on this. The reasons this is a last resort method are:

Calculators use rounded-off decimal approximations for most logarithms. So your calculator may end up telling you the answer is something like 5.00000001 or 4.99999999 instead of the 5 it should be.
This is longer and more difficult, even with a calculator, than the other methods.

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