Question

Express Y as a function of x. The constant C is a positive number. In y= In 10x + In C

Answer 1

`\ln (y)=\ln (10x)+\ln (C)`

Using the property of the addition of logs:

`\begin{gathered} \log _z(xy)=\log _z(x)+\log _z(y) \\ so\colon \\ \ln (10x)+\ln (C)=\ln (10x\cdot C)=\ln (10Cx) \end{gathered}`
`\ln (y)=\ln (10Cx)`

Take the exponential function of both sides:

`\begin{gathered} e^(\ln (y))=e^(\ln (10Cx)) \\ y=10Cx \end{gathered}`