Aloha :)
$$\left.2\cdot1,2^x=1,5\cdot1,4^{-x}\quad\right|\quad\cdot1,4^x$$$$\left.2\cdot1,2^x\cdot1,4^x=1,5\cdot1,4^{-x}\cdot1,4^x\quad\right|\quad a^x\cdot b^x=(a\cdot b)^x$$$$\left.2\cdot(1,2\cdot1,4)^x=1,5\cdot1,4^{-x}\cdot1,4^x\quad\right|\quad a^x\cdot a^y=a^{x+y}$$$$\left.2\cdot(1,2\cdot1,4)^x=1,5\cdot1,4^{-x+x}\quad\right|\quad\text{vereinfachen}$$$$\left.2\cdot1,68^x=1,5\cdot1,4^0\quad\right|\quad a^0=1$$$$\left.2\cdot1,68^x=1,5\quad\right|\quad:\,2$$$$\left.1,68^x=\frac{1,5}{2}=\frac{3}{4}\quad\right|\quad\ln(\cdots)$$$$\left.\ln(1,68^x)=\ln\left(\frac{3}{4}\right)\quad\right|\quad\ln(a^b)=b\ln a$$$$\left.x\cdot\ln(1,68)=\ln\left(\frac{3}{4}\right)\quad\right|\quad:\,\ln(1,68)$$$$\left.x=\frac{\ln\left(\frac{3}{4}\right)}{\ln(1,68)}\approx-0,55452104\quad\right.$$
~plot~ 2*1,2^x ; 1,5*1,4^(-x) ; {-0,5545|2*1,2^(-0,5545)} ; [[-4|3|0|4]] ~plot~
