помогите пожалуйста как сможете3^x+1 * 4^x=0,25 * 12^3x-1 √3^x-54 - 7 * √3^x-58 =162 6^x + 6^x+1 = 2^x + 2^x+1 + 2^x+2 9^x - 2^x+0,5 = 2^x+3,5 - 3^2x-1 5^2x-1 + 4^x = 5^2x - 4^x+1

1) [latex] 3^{x+1}* 4 = 0.25* 12^{3x-1} [/latex] [latex] 12^{x}*3= \frac{1}{4}* 12^{3x-1} [/latex] [latex] 12^{x}*3- \frac{ 12^{3x-1} }{4}=0 [/latex] [latex] 12^{x}(3- \frac{ 12^{2x-1} }{4})=0 [/latex] [latex]3- \frac{ 12^{2x-1} }{4} =0[/latex] [latex] \frac{ 12^{2x-1} }{4}=3 [/latex] [latex] 12^{2x-1}=12 [/latex] 2x-1 = 1 2x = 2 x=1 Ответ: 1 2) [latex] \sqrt{3} ^{x-54}-7* \sqrt{3} ^{x-58}=162 [/latex] [latex] \sqrt{3} ^{x-54}(1-7* (\sqrt{3}) ^{-4})=162 [/latex] [latex] \sqrt{3} ^{x-54}(1- \frac{7}{9})=162 [/latex] [latex] \sqrt{3} ^{x-54}* \frac{2}{9}=162 [/latex] [latex] \sqrt{3} ^{x-54}= \frac{162*9}{2} [/latex] [latex] 3^{ \frac{x-54}{2} }= 3^{6} [/latex] x-54 = 6*2 x-54 = 12 x = 66 Ответ: 66 3) [latex] 6^{x}+ 6^{x+1}= 2^{x}+ 2^{x+1}+ 2^{x+2} [/latex] [latex] 6^{x}(1+6) = 2^{x}(1+2+4) [/latex] [latex] 6^{x}*7 = 2^{x}*7 [/latex] [latex] 6^{x}= 2^{x} [/latex] [latex] 3^{x}=1 [/latex] x=0 Ответ: 0 4) [latex] 9^{x}- 2^{x+0.5}= 2^{x+3.5}- 3^{2x-1} [/latex] [latex] 3^{2x}+ 3^{2x-1}= 2^{x+3.5}+ 2^{x+0.5} [/latex] [latex] 3^{2x}(1+ \frac{1}{3})= 2^{x}( 2^{3.5}+ 2^{0.5}) [/latex] [latex] 3^{2x}* \frac{4}{3}= 2^{x}*9 \sqrt{2} [/latex] [latex] 3^{2x-1}* 2^{2}= 2^{x+0.5}* 3^{2} [/latex] [latex] 3^{2x-3}= 2^{x-1.5} [/latex] [latex] 3^{2x-3}= \sqrt{2} ^{2x-3} [/latex] [latex] ( \frac{3}{ \sqrt{2} }) ^{2x-3} = 1[/latex] 2x-3 = 0 2x = 3 x = 1.5 Ответ: 1,5 5) [latex] 5^{2x-1}+ 4^{x}= 5^{2x}- 4^{x+1} [/latex] [latex] 5^{2x-1}- 5^{2x}= -4^{x+1}- 4^{x} [/latex] [latex] 5^{2x}- 5^{2x-1}= 4^{x+1}+ 4^{x} [/latex] [latex] 5^{2x}(1- \frac{1}{5})= 4^{x}(4+1) [/latex] [latex] 5^{2x}* \frac{4}{5}= 4^{x}*5 [/latex] [latex] 5^{2x-1}*4= 4^{x}*5 [/latex] [latex] 5^{2x-2}= 4^{x-1} [/latex] [latex] 5^{2x-2}= 2^{2x-2} [/latex] [latex] ( \frac{5}{2}) ^{2x-2}=1 [/latex] 2x-2 = 0 2x = 2 x = 1 Ответ: 1