Как решить? 3^{x-3} + 3^{x-2} = 4

(3^x)/27 + (3^x)/9 = 4, (3^x)(1/27 + 1/9) = 4, 3^x = 27, x = 3. Ответ: 3.

[latex]3^{x-3}+3^{x-2}=4[/latex] [latex]3^x:3^3+3^x:3^2=4[/latex] [latex]3^x*3^{-3}+3^x*3^{-2}=4[/latex] [latex]3^{-3}*3^x+3^{-2}*3^x=4[/latex] [latex] \frac{1}{3^3} *3^x+ \frac{1}{3^2} *3^x=4[/latex] [latex] \frac{1}{27} *3^x+ \frac{1}{9} *3^x=4[/latex] [latex]( \frac{1}{27} + \frac{1}{9} )*3^x=4[/latex] [latex] \frac{4}{27} *3^x=4[/latex] [latex] \frac{27}{4} * \frac{4}{27} *3^x= \frac{27}{4} *4[/latex] [latex]3^x=27[/latex] [latex]3^x=3^3[/latex] [latex]x=3[/latex] Ответ: 3.