SOLUTION: write 32=2^5 in logarithmic form and evaluate log3 81 without a calculator

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Question 392319: write 32=2^5 in logarithmic form and evaluate log3 81 without a calculator
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
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
32+=+2%5E5 (an exponential equation)
we can write the following logarithmic equation:
log%282%2C+%2832%29%29+=+5

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:
3*3 = 9
3*3*3 = 27
3*3*3*3 = 81
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!