Question Number 211720 by Nadirhashim last updated on 18/Sep/24
$$\:\:\:\:\:\boldsymbol{{if}}\:\:\frac{\mathrm{8}^{\boldsymbol{{x}}} −\mathrm{2}^{\boldsymbol{{x}}} }{\mathrm{6}^{\boldsymbol{{x}}} −\mathrm{3}^{\boldsymbol{{x}}} }\:\:\:=\:\mathrm{2}\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$
Answered by Frix last updated on 18/Sep/24
$$\mathrm{obviously}\:{x}=\mathrm{1} \\ $$
Answered by BHOOPENDRA last updated on 18/Sep/24
$$\frac{\mathrm{2}^{{x}} \left(\mathrm{2}^{{x}} +\mathrm{1}\right)\left(\mathrm{2}^{{x}} −\mathrm{1}\right)}{\mathrm{3}^{{x}} \left(\mathrm{2}^{{x}} −\mathrm{1}\right)}=\mathrm{2} \\ $$$$\mathrm{2}^{{x}} \left(\mathrm{2}^{{x}} +\mathrm{1}\right)=\mathrm{2}×\:\mathrm{3}^{{x}} \\ $$$${you}\:{can}\:{put}\:{values}\:{for}\:{checking} \\ $$$${x}>\mathrm{0} \\ $$$${x}=\mathrm{1} \\ $$$$\mathrm{2}\left(\mathrm{2}+\mathrm{1}\right)=\mathrm{2}×\mathrm{3} \\ $$$$\mathrm{6}=\mathrm{6} \\ $$$${So}\:{x}=\mathrm{1} \\ $$$$ \\ $$