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Question Number 172028 by Mikenice last updated on 23/Jun/22

$$solve:$$$$\frac{{log}_2(9-2^{x)}}{{log}_2{2}^{(3-x)}}={log}_{2}2$$

Answered by Rasheed.Sindhi last updated on 23/Jun/22

$$\frac{{log}_2(9-2^{x)}}{{log}_2{2}^{(3-x)}}={log}_{2}2$$$$\frac{{log}_2(9-2^{x)}}{{log}_2{2}^{(3-x)}}=1$$$${log}_2(9-2^x)={log}_2{2}^{(3-x)}$$$$9-2^x=2^{3-x}$$$$2^x+2^{3-x}=9$$$$9issumofpowersof2$$$$9=8+1$$$$9=2^3+2^0$$$$2^x+2^{3-x}=2^3+2^0$$$$2^x+2^{3-x}=2^3+2^{3-3}$$$$x=3$$

Commented by Mikenice last updated on 23/Jun/22

$$yhankssir$$

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