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Question Number 84997 by M±th+et£s last updated on 18/Mar/20

$${log}_{\frac{x}{2}}{x}^2-{log}_{16x}{x}^3+40{log}_{4x}\sqrt{x}=0$$

Commented by jagoll last updated on 18/Mar/20

$$\frac{{\log }_2\left({\mathrm{x}}^2\right)}{{\log }_2\left(\mathrm{x}\right)-1}-\frac{{\log }_2\left({\mathrm{x}}^3\right)}{{\log }_2\left(\mathrm{x}\right)+4}+\frac{40{\log }_2\left(\sqrt{\mathrm{x}}\right)}{{\log }_2\left(\mathrm{x}\right)+2}=0$$$$\mathrm{let}{\log }_2\left(\mathrm{x}\right)=\mathrm{t}$$$$\frac{2\mathrm{t}}{\mathrm{t}-1}-\frac{3\mathrm{t}}{\mathrm{t}+4}+\frac{20\mathrm{t}}{\mathrm{t}+2}=0$$$$\mathrm{t}[\frac{2}{\mathrm{t}-1}-\frac{3}{\mathrm{t}+4}+\frac{20}{\mathrm{t}+2}]=0$$

Commented by jagoll last updated on 18/Mar/20

$$\mathrm{now}\mathrm{easy}\mathrm{to}\mathrm{solve}$$

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