find-the-value-of-x-3-x-1-2-x-2-

Question Number 8934 by j.masanja06@gmail.com last updated on 06/Nov/16

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}. \\ $$$$\mathrm{3}^{\mathrm{x}+\mathrm{1}} =\mathrm{2}^{\mathrm{x}+\mathrm{2}} \\ $$

Answered by Rasheed Soomro last updated on 08/Nov/16

3^(x+1) =2^(x+2) 3^x .3=2^x .2^2 (3^x /2^x )=(4/3) ((3/2))^x =(4/3) xlog((3/2))=log((4/3)) x=((log4−log3)/(log3−log2))≈0.7095 x≈0.7095

$$\mathrm{3}^{\mathrm{x}+\mathrm{1}} =\mathrm{2}^{\mathrm{x}+\mathrm{2}} \\ $$$$\mathrm{3}^{\mathrm{x}} .\mathrm{3}=\mathrm{2}^{\mathrm{x}} .\mathrm{2}^{\mathrm{2}} \\ $$$$\frac{\mathrm{3}^{\mathrm{x}} }{\mathrm{2}^{\mathrm{x}} }=\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{x}} =\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{xlog}\left(\frac{\mathrm{3}}{\mathrm{2}}\right)=\mathrm{log}\left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$$$\mathrm{x}=\frac{\mathrm{log4}−\mathrm{log3}}{\mathrm{log3}−\mathrm{log2}}\approx\mathrm{0}.\mathrm{7095} \\ $$$$\mathrm{x}\approx\mathrm{0}.\mathrm{7095} \\ $$

Commented by j.masanja06@gmail.com last updated on 07/Nov/16

sir remember that 2^(x+2) and not 2^(x+1)

$$\mathrm{sir}\:\mathrm{remember}\:\mathrm{that}\:\mathrm{2}^{\mathrm{x}+\mathrm{2}} \:\mathrm{and}\:\mathrm{not}\:\mathrm{2}^{\mathrm{x}+\mathrm{1}} \\ $$

Commented by Rasheed Soomro last updated on 07/Nov/16