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

Take the limit of each term.
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 limits by plugging in for all occurrences of .
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.
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)