I need to solve the equation : $\ln(x+2)+\ln(5)=\lg(2x+8)$
With the change of base formula we can turn this into: $\ln(x+2)+\ln(5)=\frac{\ln(2x+8)}{\ln(10)}$
We can also simplify the LHS with the product rule so: $\ln(5(x+2))=\frac{\ln(2x+8)}{\ln(10)}$
Solving the fraction gives us: $\ln(10) \, \ln(5(x+2)) = \ln(2x+8)$
Simplifying the LHS even further: $\ln(5x+10)^{\ln(10)}=\ln(2x+8)$
We can then see that $(5x+10)^{\ln(10)}=2x+8$
And this is where I get stuck, I can't seem to figure out how to expand this term. Does anyone know how to solve this?