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:

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