Aloha :)
$$3,5^{\red{1-x}}\cdot3,5^{\green{2x}}=100\quad\big|\text{Verwende }a^{\red b}\cdot a^{\green c}=a^{\red{b}+\green{c}}$$$$3,5^{\red{1-x}+\green{2x}}=100\quad\big|\text{Exponent vereinfachen}$$$$3,5^{1+x}=100\quad\big|\text{Verwende wieder }a^{\red b}\cdot a^{\green c}=a^{\red{b}+\green{c}}\text{, aber rückwärts}$$$$3,5^1\cdot3,5^x=100\quad\big|\div3,5$$$$3,5^x=\frac{100}{3,5}=\frac{200}{7}\quad\bigg|\ln(\cdots)$$$$\ln\left(3,5^x\right)=\ln\left(\frac{200}{7}\right)\quad\bigg|\text{Verwende }\ln(a^b)=b\cdot\ln(a)$$$$x\cdot\ln(3,5)=\ln\left(\frac{200}{7}\right)\quad\bigg|\div\ln(3,5)$$$$x=\frac{\ln\left(\frac{200}{7}\right)}{\ln(3,5)}\approx2,6760$$
