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if-8-x-2-x-6-x-3-x-2-find-x-




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

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