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How do you expand #lnsqrt(a-1) #?

Answer 1

Caleb Alexander

#=> ln(a - 1)^(1/2)#

Use the rule #loga^n = nloga# to simplify.

#=>1/2ln(a - 1)#

This is as far as you can simplify.

Hopefully this helps!

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Answer 2

Serenity Jones

To expand ln(sqrt(a - 1)), you can first rewrite the expression using properties of logarithms and exponents.

ln(sqrt(a - 1)) = ln((a - 1)^(1/2))

Then, using the property that ln(a^b) = b * ln(a), you can bring the exponent down:

ln((a - 1)^(1/2)) = (1/2) * ln(a - 1)

So, ln(sqrt(a - 1)) expands to (1/2) * ln(a - 1).

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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.