Question

solve the following equation for x. Round any decimal to the nearest hundredth place ln 4^(x+3)= ln3^-3

Answer 1

`\ln 4^(x+3)=\ln 3^(-x)`

Using the properties of logarithms we have that:

`\begin{gathered} 4^(x+3)=3^(-x) \\ \log _2(4^(x+3))=\log _2(3^(-x)) \\ 2(x+3)=-x\log _2(3) \\ 2x+6=-x\log _2(3) \\ 2x+x\log _2(3)=-6 \\ x(2+\log _2(3))=-6 \\ x=-(6)/(2+\log _2(3)) \end{gathered}`

x has a value of -6/(2+log₂(3))