document.write( "Question 392319: write 32=2^5 in logarithmic form and evaluate log3 81 without a calculator \n" ); document.write( "

Algebra.Com's Answer #278663 by jsmallt9(3758) $\"\"$ $\"About$

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In general $\"log%28p%2C+%28q%29%29+=+z\"$ (a logarithmic equation) is equivalent to $\"q+=+p%5Ez\"$ (an exponential equation. Using this pattern on
\n" ); document.write( " $\"32+=+2%5E5\"$ (an exponential equation)
\n" ); document.write( "we can write the following logarithmic equation:
\n" ); document.write( " $\"log%282%2C+%2832%29%29+=+5\"$

\n" ); document.write( "Logarithms can be found without a calculator if the argument is a known power of the base of the logarithm. So we want to see if 81 is a power of 3. Multiplying 3's to together we get:
\n" ); document.write( "3*3 = 9
\n" ); document.write( "3*3*3 = 27
\n" ); document.write( "3*3*3*3 = 81
\n" ); document.write( "So 81 is $\"3%5E4\"$ . Since $\"log%283%2C+%2881%29%29\"$ represents the exponent for 3 that results in 81 we now know that the answer is 4! \n" ); document.write( "

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