Question-210607

Question Number 210607 by peter frank last updated on 13/Aug/24

Answered by A5T last updated on 14/Aug/24

75(5^(3log_2 x) )=75(2^(log_2 5) )^(log_2 x×3) =75(2^(log_2 x) )^(3log_2 5) =75(x)^(3log_2 5) =4x ⇒x^(log_2 (((125)/2))) =(4/(75))⇒x=((4/(75)))^(1/(log_2 (125)−1)) ≈0.6118

$$\mathrm{75}\left(\mathrm{5}^{\mathrm{3}{log}_{\mathrm{2}} {x}} \right)=\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} \mathrm{5}} \right)^{{log}_{\mathrm{2}} {x}×\mathrm{3}} =\mathrm{75}\left(\mathrm{2}^{{log}_{\mathrm{2}} {x}} \right)^{\mathrm{3}{log}_{\mathrm{2}} \mathrm{5}} \\ $$$$=\mathrm{75}\left({x}\right)^{\mathrm{3}{log}_{\mathrm{2}} \mathrm{5}} =\mathrm{4}{x} \\ $$$$\Rightarrow{x}^{{log}_{\mathrm{2}} \left(\frac{\mathrm{125}}{\mathrm{2}}\right)} =\frac{\mathrm{4}}{\mathrm{75}}\Rightarrow{x}=\left(\frac{\mathrm{4}}{\mathrm{75}}\right)^{\frac{\mathrm{1}}{{log}_{\mathrm{2}} \left(\mathrm{125}\right)−\mathrm{1}}} \approx\mathrm{0}.\mathrm{6118} \\ $$

Commented by peter frank last updated on 14/Aug/24