Решить уравнения 1) 7x = 343 2) 6x+3=216 3) (+)=572 4) 46x-4096 5) 552-5 6) (1/242-256 7) 32x=16 8) 81x+4= 27 9) 125 = 25 10) 6426 11) 16x=32 5x 28 12) (+)=243 13) 492=54 14) (+) x+/-64 15 2862+P 16) 2x+3 32+5-216 3x.81=243

Привет! Разберем эти уравнения вместе, чтобы тебе все стало понятно. Логика такая: нам нужно привести обе части уравнения к одному основанию и потом приравнять показатели степеней. Поехали! 1) \(7^x = 343\) \(7^x = 7^3\) \(x = 3\) 2) \(6^{x+3} = 216\) \(6^{x+3} = 6^3\) \(x+3 = 3\) \(x = 0\) 3) \((\frac{1}{8})^x = 512\) \((2^{-3})^x = 2^9\) \(2^{-3x} = 2^9\) \(-3x = 9\) \(x = -3\) 4) \(4^{6x} = 4096\) \(4^{6x} = 4^6\) \(6x = 6\) \(x = 1\) 5) \(5^{x-5} = 625\) \(5^{x-5} = 5^4\) \(x-5 = 4\) \(x = 9\) 6) \((\frac{1}{16})^{x+2} = 256\) \((2^{-4})^{x+2} = 2^8\) \(2^{-4x-8} = 2^8\) \(-4x-8 = 8\) \(-4x = 16\) \(x = -4\) 7) \(32^x = 16\) \((2^5)^x = 2^4\) \(2^{5x} = 2^4\) \(5x = 4\) \(x = \frac{4}{5}\) 8) \(81^{x+4} = 27\) \((3^4)^{x+4} = 3^3\) \(3^{4x+16} = 3^3\) \(4x+16 = 3\) \(4x = -13\) \(x = -\frac{13}{4}\) 9) \(125^x = \frac{1}{25}\) \((5^3)^x = 5^{-2}\) \(5^{3x} = 5^{-2}\) \(3x = -2\) \(x = -\frac{2}{3}\) 10) \(64^{x-6} = 8\) \((2^6)^{x-6} = 2^3\) \(2^{6x-36} = 2^3\) \(6x-36 = 3\) \(6x = 39\) \(x = \frac{13}{2}\) 11) \(16^x = 32\) \((2^4)^x = 2^5\) \(2^{4x} = 2^5\) \(4x = 5\) \(x = \frac{5}{4}\) 12) \((\frac{1}{3})^{5x} = 243\) \((3^{-1})^{5x} = 3^5\) \(3^{-5x} = 3^5\) \(-5x = 5\) \(x = -1\) 13) \(49^x = 343\) \((7^2)^x = 7^3\) \(7^{2x} = 7^3\) \(2x = 3\) \(x = \frac{3}{2}\) 14) \((\frac{1}{4})^{x+4} = 64\) \((4^{-1})^{x+4} = 4^3\) \(4^{-x-4} = 4^3\) \(-x-4 = 3\) \(-x = 7\) \(x = -7\) 15) \(256^{x+1} = 16\) \((2^8)^{x+1} = 2^4\) \(2^{8x+8} = 2^4\) \(8x+8 = 4\) \(8x = -4\) \(x = -\frac{1}{2}\) 16) \(2^{x+3} \cdot 3^{x+3} = 216\) \((2 \cdot 3)^{x+3} = 6^3\) \(6^{x+3} = 6^3\) \(x+3 = 3\) \(x = 0\) 17) \(3^x \cdot 81 = 243\) \(3^x \cdot 3^4 = 3^5\) \(3^{x+4} = 3^5\) \(x+4 = 5\) \(x = 1\)