SOLUTION: solve 4^2x-3 = 1/16

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Question 151075: solve 4^2x-3 = 1/16
Answer by jim_thompson5910(35256) About Me  (Show Source):
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4%5E%282x-3%29+=+1%2F16 Start with the given equation.


%282%5E2%29%5E%282x-3%29+=+1%2F16 Rewrite 4 as 2%5E2


2%5E%282%282x-3%29%29+=+1%2F16 Multiply the exponents.


2%5E%282%282x-3%29%29+=+2%5E%28-4%29 Rewrite 1%2F16 as 16%5E%28-1%29=%282%5E4%29%5E%28-1%29=2%5E%28%284%29%28-1%29%29=2%5E%28-4%29


2%282x-3%29=-4 Since the bases are equal, this means that the exponents are equal.


4x-6=-4 Distribute.


4x=-4%2B6 Add 6 to both sides.


4x=2 Combine like terms on the right side.


x=%282%29%2F%284%29 Divide both sides by 4 to isolate x.


x=1%2F2 Reduce.


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Answer:

So the answer is x=1%2F2


Which approximates to x=0.5