what is the true solution to the equation below?\n$ln e^{ln x}+ln e^{ln x^{2}} = 2ln 8$\n$x = 2$\n$x =…

Explanation:

Step1: Use the property $\ln e^a=a$

$\ln e^{\ln x}+\ln e^{\ln x^{2}}=\ln x+\ln x^{2}$

Step2: Use the property $\ln a^{b}=b\ln a$ for $\ln x^{2}$

$\ln x+\ln x^{2}=\ln x + 2\ln x=3\ln x$

Step3: Rewrite the right - hand side using the property $b\ln a=\ln a^{b}$

$2\ln 8=\ln 8^{2}=\ln 64$

Step4: Solve the equation

Since $3\ln x=\ln 64$, and $3\ln x=\ln x^{3}$, then $\ln x^{3}=\ln 64$. So $x^{3}=64$, and $x = 4$.

Answer:

$x = 4$