Question Number 116907 by math35 last updated on 07/Oct/20
Answered by Lordose last updated on 07/Oct/20
$$\mathrm{2}^{\mathrm{x}+\mathrm{2}} \:×\:\mathrm{2}^{\mathrm{3}\left(\mathrm{2x}−\mathrm{3}\right)} \:=\:\mathrm{2}^{\mathrm{10}} \\ $$$$\mathrm{2}^{\mathrm{x}+\mathrm{2}+\mathrm{6x}−\mathrm{9}} \:=\:\mathrm{2}^{\mathrm{10}} \\ $$$$\mathrm{7x}−\mathrm{7}=\mathrm{10} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{17}}{\mathrm{7}} \\ $$
Answered by Olaf last updated on 07/Oct/20
$$\left({x}+\mathrm{2}\right)\mathrm{ln2}+\left(\mathrm{2}{x}−\mathrm{3}\right)\mathrm{ln8}\:=\:\mathrm{ln1024} \\ $$$$\left({x}+\mathrm{2}\right)\mathrm{ln2}+\mathrm{3}\left(\mathrm{2}{x}−\mathrm{3}\right)\mathrm{ln2}\:=\:\mathrm{10ln2} \\ $$$$\mathrm{7}{x}\:=\:\mathrm{17} \\ $$$${x}\:=\:\frac{\mathrm{17}}{\mathrm{7}} \\ $$