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November 1st, 2015, 02:26 PM   #1
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Expanding and simplifying logarithms

So there is no way to know how to do this unless you know some complicated algebraic rules. For example, square root is somehow the same thing as raised to the power of 1/2. To get rid of a denominator, change the sign of the exponent and multiply it to the numerator. Bring down the exponent in front of the LN or LOG. Log mn is equal to log m- log n. Log(1) =0. Despite knowing all these things, I have no idea how to do expand and simplify this equation. Do I need to know more? (Goodness).

So I'm stuck with $\displaystyle \log square root of x+1/x^2+1$

So what I did was change that square root to x+1^1/2.
Then I brought the denominator up by subtracting it to the numerator. So now I have

$\displaystyle \log(x+1)^{1/2}-x^2+1$. I'm wrong by the way. I don't know why. Help please.

Last edited by skipjack; November 1st, 2015 at 05:25 PM.
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November 1st, 2015, 03:03 PM   #2
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What you have posted is

$\log{\sqrt{x}} + \dfrac{1}{x^2} +1$

Is that what you meant?
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November 1st, 2015, 05:33 PM   #3
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$\displaystyle \log\frac{\sqrt{x+1}}{x^2+1} = \log(x+1)^{1/2} + \log\left(x^2+1\right)^{-1} = \frac12\log(x + 1) - \log\left(x^2+1\right)$
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