SOLUTION: 4 to the k-2=8 to the 12-k. solve for k

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Question 388347: 4 to the k-2=8 to the 12-k. solve for k
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%28k-2%29=8%5E%2812-k%29 Start with the given equation.


%282%5E2%29%5E%28k-2%29=8%5E%2812-k%29 Rewrite 4 as 2%5E2


%282%5E2%29%5E%28k-2%29=%282%5E3%29%5E%2812-k%29 Rewrite 8 as 2%5E3


2%5E%282%28k-2%29%29=2%5E%283%2812-k%29%29 Multiply the exponents.


2%28k-2%29=3%2812-k%29 Since the bases are equal, the exponents are equal.


2k-4=36-3k Distribute.


2k=36-3k%2B4 Add 4 to both sides.


2k%2B3k=36%2B4 Add 3k to both sides.


5k=36%2B4 Combine like terms on the left side.


5k=40 Combine like terms on the right side.


k=%2840%29%2F%285%29 Divide both sides by 5 to isolate k.


k=8 Reduce.


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Answer:

So the solution is k=8


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