SOLUTION: Hello, Could you please assist me with solving the following equation for x: log x = -1/6 64 Thank You

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Question 374721: Hello,
Could you please assist me with solving the following equation for x:
log x = -1/6
64
Thank You
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that we can rewrite log%28b%2C%28x%29%29=y as x=b%5Ey


So this means that we can rewrite log%2864%2C%28x%29%29=-1%2F6 as x=64%5E%28-1%2F6%29%5E%22%22


x=64%5E%28-1%2F6%29%5E%22%22 Start with the given equation.


x=%282%5E6%29%5E%28-1%2F6%29%5E%22%22 Rewrite 64 as 2%5E6


x=2%5E%286%28-1%2F6%29%29%5E%22%22 Use the identity %28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29


x=2%5E%28-6%2F6%29%5E%22%22 Multiply


x=2%5E%28-1%29 Reduce.


x=1%2F2%5E%281%29 Flip the base to make the exponent positive.


x=1%2F2 Evaluate 2%5E1 to get 2.


So the solution is x=1%2F2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim