SOLUTION: log8 (32) please help me solve

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Question 381648: log8 (32)
please help me solve
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%288%2C+%2832%29%29
With expressions like this you want to look to see if
  • the base is an obvious power of the argument, or
  • the argument is an obvious power of the base, or
  • the base and the argument are both obvious powers of some other number.

It is not obvious what power of 8 32 is. Nor is it obvious what power of 32 8 is. But with a little work we can find that 8 and 32 are both powers of 2. So we can simplify this expression "by hand" if we 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 the base 8 logarithm into an expression of base 2 logarithms:
log%282%2C+%2832%29%29%2Flog%282%2C+%288%29%29
Since 32+=+2%5E5 then log%282%2C+%2832%29%29+=+5. Similarly, since 8+=+2%5E3 then log%282%2C+%288%29%29+=+3. This makes our expression:
5/3