SOLUTION: Which of the following expressions is equivalent to 0.5(log(2)(x+1)-log(2)(x^2+2x+1)), where x can not equal -1? 2 = base of the logarithm a. log(2)sqrt(1/x+1) b. log(2)sqrt(

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Which of the following expressions is equivalent to 0.5(log(2)(x+1)-log(2)(x^2+2x+1)), where x can not equal -1? 2 = base of the logarithm a. log(2)sqrt(1/x+1) b. log(2)sqrt(      Log On


   

Question 944210: Which of the following expressions is equivalent to 0.5(log(2)(x+1)-log(2)(x^2+2x+1)), where x can not equal -1? 2 = base of the logarithm
a. log(2)sqrt(1/x+1)
b. log(2)sqrt(x+1)
c. log(2)((x^2+2x+1)(x+1))
d. -3log(2)x
How do I go about solving a question like this, trying to find examples but I am struggling to find any, if someone could give me a step by step breakdown that would be greatly appreciated.
Thank you
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Which of the following expressions is equivalent to 0.5(log(2)(x+1)-log(2)(x^2+2x+1)), where x can not equal -1? 2 = base of the logarithm
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0.5(log(2)(x+1)-log(2)(x^2+2x+1)
= 0.5[log2[(x+1)/(x^2+2x+1)]]
----
= 0.5[log2[(x+1)/(x+1)^2]]
----
= 0.5[log2[1/(x+1)]]
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= log2[sqrt[1/(x+1)]]
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Cheers,
Stan H.
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a. log(2)sqrt(1/x+1)
b. log(2)sqrt(x+1)
c. log(2)((x^2+2x+1)(x+1))
d. -3log(2)x

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
0.5(log(2)(x+1)-log(2)(x^2+2x+1))
= 0.5%2A%28log%282%2C%28x%2B1%29%29+-+log%282%2C%28x%5E2%2B2x%2B1%29%29%29
---
= 0.5%2A%28log%282%2C%28x%2B1%29%29+-+log%282%2C%28x%2B1%29%5E2%29%29
Subtracting logs --> division
= 0.5%2A%28log%282%2C%28x%2B1%29%2F%28%28x%2B1%29%5E2%29%29%29
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= 0.5%2Alog%282%2C%281%2F%28x%2B1%29%29%29
= log%282%2C%281%2Fsqrt%28x%2B1%29%29%29
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Same as choice a.