identify the solution set of 3 ln 4 = 2 ln x.\n{6}\n{-8, 8}\n{8}\ndone

Explanation:

Step1: Use logarithm property

Using the power - rule of logarithms (a\ln b=\ln(b^{a})), we can rewrite the left - hand side as (\ln(4^{3})) and the right - hand side as (\ln(x^{2})). So, (3\ln4 = 2\ln x) becomes (\ln(4^{3})=\ln(x^{2})), which simplifies to (\ln64=\ln(x^{2})).

Step2: Remove the logarithms

Since the natural logarithm function (y = \ln u) is one - to - one, if (\ln a=\ln b), then (a = b). So, (x^{2}=64).

Step3: Solve for (x)

Taking the square root of both sides, we get (x=\pm8). But the domain of the natural logarithm function (y = \ln x) is (x>0). So, we discard (x = - 8).

Answer:

({8})