solve for x to get a solution set

Algebra
Tutor: None Selected Time limit: 1 Day

Jul 15th, 2015

Thank you for the opportunity to help you with your question!

So your expression, log%283%2C+%28sqrt%2827%29%29%29, is read as "base 3 logarithm of 27" we should be thinking of it as "the exponent for 3 that results in sqrt%2827%29 So your problem is to figure out what power of 3 results in sqrt%2827%29. If you know that 27=+3%5E3 and if you're really good with exponents you will already know the answer. If you don't know the answer yet, then try to express sqrt%2827%29 as a power of 3. Well, we can start by writing the 27 as a power of 3:


sqrt%2827%29+=+sqrt%283%5E3%29
But what about the square root? Square roots are powers of 1/2. IOW, sqrt%28x%29+=+x%5E%281%2F2%29. So we can rewrite our square root as an exponent of 1/2:
sqrt%2827%29+=+sqrt%283%5E3%29+=+%283%5E3%29%5E%281%2F2%29
The rule for exponents when raising a power to a power is to multiply the exponents:

We can now see what exponent on 3 results in sqrt%2827%29! An exponent of 3/2 on a 3 results in sqrt%2827%29. So
log%283%2C+%28sqrt%2827%29%29%29+=+3%2F2
Please let me know if you nea case for torture by michale levined any clarification. I'm always happy to answer your questions.
Jul 15th, 2015

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