<PRE><B>Question 283578</B>
*[Tex \LARGE 4^{3x+2}=7^{x-3}]



*[Tex \LARGE \ln\left(4^{3x+2}\right)=\ln\left(7^{x-3}\right)]



*[Tex \LARGE (3x+2)\ln\left(4\right)=(x-3)\ln\left(7\right)]



*[Tex \LARGE 3x\ln\left(4\right)+2\ln\left(4\right)=x\ln\left(7\right)-3\ln\left(7\right)]



*[Tex \LARGE 3x\ln\left(4\right)-x\ln\left(7\right)=-3\ln\left(7\right)-2\ln\left(4\right)]



*[Tex \LARGE x\left(3\ln\left(4\right)-\ln\left(7\right)\right)=-3\ln\left(7\right)-2\ln\left(4\right)]



*[Tex \LARGE x=\frac{-3\ln\left(7\right)-2\ln\left(4\right)}{3\ln\left(4\right)-\ln\left(7\right)}]



*[Tex \LARGE x\approx-3.890837992]</PRE>