Question

Can someone help me with this problem?

Answer 1

`~~~~~\frac 13 \ln\left(x^6 \right) +\frac 12 \ln\left(x^2\right) = \ln x^a\\\\\implies \ln \left(x^6 \right)^(\tfrac 13) + \ln \left(x^2 \right)^(\tfrac 12) = \ln x^a\\ \\\implies \ln x^2 + \ln x = \ln x^a\\\\\implies \ln(x^2 \cdot x) = \ln x^a \\\\\implies \ln x^3 = \ln x^a\\ \\\implies 3 \ln x = a \ln x\\\\\implies a =3`