SOLUTION: My son submitted the following 2 questions earlier: log base 2 square root 8 and 5^1-2x=1/5 We have the solutions for these but no explanation. Neither of us can figure eith

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: My son submitted the following 2 questions earlier: log base 2 square root 8 and 5^1-2x=1/5 We have the solutions for these but no explanation. Neither of us can figure eith      Log On


   

Question 925480: My son submitted the following 2 questions earlier:
log base 2 square root 8 and
5^1-2x=1/5
We have the solutions for these but no explanation. Neither of us can figure either out. Can you help us, please?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.


log%282%2C%28sqrt%288%29%29%29+=+log%28%28sqrt%288%29%29%29%2Flog%28%282%29%29 Use the change of base formula


Convert to rational exponent form (sqrt%28x%29+=+x%5E%281%2F2%29%5E%22%22)


log%282%2C%28sqrt%288%29%29%29+=+%28%281%2F2%29log%28%288%29%29%29%2Flog%28%282%29%29 Use log rule 3


log%282%2C%28sqrt%288%29%29%29+=+%28%281%2F2%29log%28%282%5E3%29%29%29%2Flog%28%282%29%29 Rewrite 8 as 2^3


log%282%2C%28sqrt%288%29%29%29+=+%28%281%2F2%29%2A3%2Alog%28%282%29%29%29%2Flog%28%282%29%29 Use log rule 3


log%282%2C%28sqrt%288%29%29%29+=+%28%283%2F2%29%2Alog%28%282%29%29%29%2Flog%28%282%29%29 Multiply


Highlight common terms


Cancel common terms


log%282%2C%28sqrt%288%29%29%29+=+%28%283%2F2%29%2A1%29%2F%281%29


log%282%2C%28sqrt%288%29%29%29+=+3%2F2