Answer:
ln(x)/2 -3.810930
Step-by-step explanation:
The relevant rules of logarithms are ...
ln(ab) = ln(a) +ln(b)
ln(a^b) = b·ln(a)
ln(a/b) = ln(a) -ln(b)
ln(e) = 1
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Your expression expands to ...
[tex]\ln\left(\dfrac{4\sqrt{x}}{9e^3}\right) = \ln(4\sqrt{x})-\ln(9e^3)=\ln(4)+\dfrac{1}{2}\ln(x)-(\ln(9)+3\ln(e))\\\\=\dfrac{1}{2}\ln(x)+\ln(4)-\ln(9)-3\\\\\approx\dfrac{\ln(x)}{2}-3.810930[/tex]
