решить уравнение:(13^15:13^4):(x-17)=13^9. Created by pirquliyevasabina. algebra-ru

решить уравнение:(13^15:13^4):(x-17)=13^9...

Ответ:

$\frac{( {13}^{15} \div {13}^{4} )}{x - 17} = {13}^{9} \\ \frac{ {13}^{15 - 4} }{x - 17} = {13}^{9} \\ \frac{ {13}^{11} }{x - 17} = {13}^{9} \\ (x - 17) \times {13}^{9} = {13}^{11} \\ x - 17 = \frac{ {13}^{11} }{ {13}^{9} } \\ x - 17 = {13}^{11 - 9} \\ x - 17 = {13}^{2} \\ x - 17 = 169 \\ x = 169 + 17 \\ x = 186$

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FbifMillenium

Ответ:

(13^15:13^4):(x-17)=13^9=

$(13^{15}:13^{4}):(x-17)=13^{9};\\\\(13^{15-4}):(x-17)=13^{9}; \\\\(13^{11}):(x-17)=13^{9}; \\\\\frac{13^{11} }{x-17} =13^{9}; |*(x-17)\\\\(x-17)*\frac{13^{11} }{x-17} =13^{9}*(x-17);\\\\13^{11} =13^{9}*(x-17); |:13^{9} \\\\13^{11}: 13^{9} =13^{9}*(x-17):13^{9} ;\\\\13^{11-9}=x-17;\\\\13^{2}=x-17;\\\\169=x-17;\\\\-x=-17-169;\\\\-x=-186;\\\\x=186.$

В 4-ой строке умножаем обе части уравнения на (x - 17).

В 6-ой строке делим обе части уравнения на $13^{9}$ .

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