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Question Number 8905 by j.masanja06@gmail.com last updated on 04/Nov/16

find the value of x 3^x =9x

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{3}^{\mathrm{x}} \:=\mathrm{9x} \\ $$

Answered by Rasheed Soomro last updated on 04/Nov/16

3^x =9x⇒x=3^(x−2) Obviously x is comprised of factor 3 only. I-E x=3,9,27,... Can be easily verified that only x=3 satisfy: x=3^(x−2) ⇒3=3^(3−2) ⇒3=3 Or 3^x =9x⇒3^3 =9(3)⇒27=27 Hence x=3

$$\mathrm{3}^{\mathrm{x}} \:=\mathrm{9x}\Rightarrow\mathrm{x}=\mathrm{3}^{\mathrm{x}−\mathrm{2}} \\ $$$$\mathrm{Obviously}\:\mathrm{x}\:\mathrm{is}\:\mathrm{comprised}\:\mathrm{of}\:\mathrm{factor}\:\mathrm{3}\:\mathrm{only}. \\ $$$$\mathrm{I}-\mathrm{E}\:\mathrm{x}=\mathrm{3},\mathrm{9},\mathrm{27},... \\ $$$$\mathrm{Can}\:\mathrm{be}\:\mathrm{easily}\:\mathrm{verified}\:\mathrm{that}\:\mathrm{only}\:\mathrm{x}=\mathrm{3}\:\mathrm{satisfy}: \\ $$$$\mathrm{x}=\mathrm{3}^{\mathrm{x}−\mathrm{2}} \Rightarrow\mathrm{3}=\mathrm{3}^{\mathrm{3}−\mathrm{2}} \Rightarrow\mathrm{3}=\mathrm{3} \\ $$$$\mathrm{Or}\:\mathrm{3}^{\mathrm{x}} \:=\mathrm{9x}\Rightarrow\mathrm{3}^{\mathrm{3}} =\mathrm{9}\left(\mathrm{3}\right)\Rightarrow\mathrm{27}=\mathrm{27} \\ $$$$\mathrm{Hence}\:\mathrm{x}=\mathrm{3} \\ $$$$ \\ $$

Commented by mrW last updated on 11/Nov/16

there is an other solution x≈0.12785

$$\mathrm{there}\:\mathrm{is}\:\mathrm{an}\:\mathrm{other}\:\mathrm{solution}\:\mathrm{x}\approx\mathrm{0}.\mathrm{12785} \\ $$

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