1. I'll list the properties of logarithms and I'll do one as a model for the others.

b)

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2.

The question said that you need to take a common factor of the smaller exponent. Obviously, you can see that x-1 is common, so take the one with the smaller exponent.

Now simplify.

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3. First, you need to combine the fractions in the numerator.

Their Least Common Denominator is x(x+1). Here's how you combine them:

Can you continue?

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4. Take a look at this post.

http://www.mathhelpforum.com/math-he...980-post2.html

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5 & 6. I'll list the properties of exponents just in case you don't remember them:

Also, remember the principal of powers:

If a = b, then

Alrighty now? Let's go back to the original question:

Now, let's get rid of the fractional exponent by cubing both sides.

So this becomes a quadratic form:

Now, we have to solve for x. Use the quadratic formula:

Now, for number 6: look again at the properties of exponents. What did I say a^0 equals to?