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How do you expand #ln(x/sqrt(x^6+3))#?

Answer 1

Serenity Jones

The expression can be simplified to #lnx - 1/2ln(x^6 + 3)#

Start by applying the rule #log_a(n/m) = log_a(n) - log_a(m)#.

#=>ln(x) - ln(sqrt(x^6 + 3))#

Write the #√# in exponential form.

#=> lnx - ln(x^6 + 3)^(1/2)#

Now, use the rule #log(a^n) = nloga#.

#=>lnx - 1/2ln(x^6 + 3)#

This is as far as we can go.

Hopefully this helps!

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Answer 2

Sadie Alexander

To expand ln(x/sqrt(x^6+3)), first, rewrite the expression inside the natural logarithm as a product of powers. Then use the properties of logarithms to simplify the expression.

ln(x/sqrt(x^6+3)) = ln(x) - ln(sqrt(x^6+3))

Using the property ln(ab) = ln(a) + ln(b), the expression can be further simplified:

ln(x) - ln(sqrt(x^6+3)) = ln(x) - (1/2) * ln(x^6 + 3)

So, ln(x/sqrt(x^6+3)) expands to ln(x) - (1/2) * ln(x^6 + 3).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.