Split the limit using the Limits Quotient Rule on the limit as approaches .

Move the limit inside the logarithm.

Move the term outside of the limit because it is constant with respect to .

Move the limit under the radical sign.

Move the term outside of the limit because it is constant with respect to .

Evaluate the limit of by plugging in for .

Evaluate the limit of by plugging in for .

Multiply by .

Simplify the denominator.

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

Combine and simplify the denominator.

Multiply and .

Move .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Evaluate limit as x approaches 8 of ( natural log of 3x)/( square root of 3x)