Question

What is the true solution?

ln e^(ln x)+ln e^(ln x^2)=2 ln 8

Answer 1

It is 4 or B

Explanation:

I took the test

Answer 2

Assuming
`x` is real:


`\ln e^(\ln x) = \ln x\cdot\ln e=\ln x`


`\ln e^(\ln x^2) = \ln x^2\cdot\ln e = \ln x^2 = 2\ln x`


So


`\ln e^(\ln x)+\ln e^(\ln x^2)=2\ln 8\iff\ln x+2\ln x=3\ln x=2\ln 8`


`\implies\ln x=\frac23\ln 8=\ln 8^(2/3)`


`\implies x=e^{\ln 8^(2/3)}=8^(2/3)=(8^2)^(1/3)=64^(1/3)=4`