Question Number 152805 by mathlove last updated on 01/Sep/21
Answered by MJS_new last updated on 01/Sep/21
$${x}\geqslant\mathrm{0} \\ $$$$\mathrm{3ln}\:\mathrm{2}\:{x}=\mathrm{7ln}\:\mathrm{2}\:\sqrt{{x}} \\ $$$$\mathrm{3}{x}=\mathrm{7}\sqrt{{x}} \\ $$$${x}=\mathrm{0}\vee{x}=\frac{\mathrm{49}}{\mathrm{9}} \\ $$
Answered by JDamian last updated on 01/Sep/21
$$\mathrm{2}^{\mathrm{3}{x}} =\mathrm{2}^{\mathrm{7}\sqrt{{x}}} \\ $$$$\mathrm{3}{x}=\mathrm{7}\sqrt{{x}} \\ $$$$\mathrm{9}{x}^{\mathrm{2}} −\mathrm{49}{x}=\mathrm{0}\:\:\Rightarrow\:\begin{cases}{{x}=\mathrm{0}}\\{\mathrm{9}{x}−\mathrm{49}=\mathrm{0}\:\:\Rightarrow\:{x}=\frac{\mathrm{49}}{\mathrm{9}}=\left(\frac{\mathrm{7}}{\mathrm{3}}\right)^{\mathrm{2}} }\end{cases}\: \\ $$
Commented by otchereabdullai@gmail.com last updated on 08/Sep/21
$$\mathrm{nice}\:\mathrm{one}! \\ $$