SOLUTION: 1000^8x=100 x=5/32 Am I correct?

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Question 191772This question is from textbook saxon algebra 2
: 1000^8x=100
x=5/32
Am I correct? This question is from textbook saxon algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1000%5E%288x%29=100 Start with the given equation.


%2810%5E3%29%5E%288x%29=10%5E2 Rewrite 1000 as 10%5E3 and 100 as 10%5E2


10%5E%283%288x%29%29=10%5E2 Multiply the exponents.


10%5E%2824x%29=10%5E2 Multiply


24x=2 Since the bases are equal, this means that the exponents are equal.


x=%282%29%2F%2824%29 Divide both sides by 24 to isolate x.


x=1%2F12 Reduce.


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Answer:

So the answer is x=1%2F12 which approximates to x=0.083.