SOLUTION: logx (x^2 - x + 4) = 2 3 + log 3 243 = 3x - 4

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Question 187010: logx (x^2 - x + 4) = 2
3 + log 3 243 = 3x - 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%2C%28x%5E2+-+x+%2B+4%29%29=2 Start with the given equation.


x%5E2=x%5E2+-+x+%2B+4 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


x%5E2-x%5E2+%2B+x+=+4 Subtract x%5E2 from both sides. Add "x" to both sides.


x+=+4 Combine like terms.



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Answer:

So the answer is x=4





# 2


3+%2B+log%283%2C%28243%29%29+=+3x+-+4 Start with the given equation.


3+%2B+log%283%2C%283%5E5%29%29+=+3x+-+4 Rewrite 243 as 3%5E5


3+%2B+5%2Alog%283%2C%283%29%29+=+3x+-+4 Rewrite the log using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


3+%2B+5%281%29+=+3x+-+4 Evaluate the log base 3 of 3 to get 1


3+%2B+5+=+3x+-+4 Multiply


8=3x-4 Combine like terms on the left side.


8%2B4=3x Add 4 to both sides.


12=3x Combine like terms.


12%2F3=x Divide both sides by 3.


4=x Reduce



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Answer:

So the answer is x=4