solve: 4 ln x = 2 ln 25\nx = 5\nx = 25\nx = 625

Answer:

A. ( x = 5 )

Explanation:

Step1: Use the logarithmic property ( n\ln a=\ln(a^{n}))

$$4\ln x=\ln(x^{4}),\quad 2\ln25 = \ln(25^{2})=\ln625$$ The equation (4\ln x = 2\ln25) becomes (\ln(x^{4})=\ln625)

Step2: Use the property if (\ln a=\ln b), then (a = b)

Since (\ln(x^{4})=\ln625), we have (x^{4}=625)

Step3: Solve for (x)

Take the fourth - root of both sides. (x=\sqrt[4]{625}) We know that (625 = 5^{4}), so (x = 5) (we consider the positive root since the domain of (y = \ln x) is (x>0))