Объяснение:
0\hfill\\x-3>0\hfill\\x-3\ne1\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}x>-1\hfill\\x>3\hfill\\x\ne4\hfill\\\end{gathered}\right.\hfill\\\boxed{x\in(3;+\infty)}\hfill\\\end{gathered}\]" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5C%5B%5Cbegin%7Bgathered%7D2%29%5C%3B%5C%3B%7B%5Clog_%7Bx-3%7D%7D%28x%2B1%29%5Chfill%5C%5C%5Cleft%5C%7B%5Cbegin%7Bgathered%7Dx%2B1%3E0%5Chfill%5C%5Cx-3%3E0%5Chfill%5C%5Cx-3%5Cne1%5Chfill%5C%5C%5Cend%7Bgathered%7D%5Cright.%5CLeftrightarrow%5Cleft%5C%7B%5Cbegin%7Bgathered%7Dx%3E-1%5Chfill%5C%5Cx%3E3%5Chfill%5C%5Cx%5Cne4%5Chfill%5C%5C%5Cend%7Bgathered%7D%5Cright.%5Chfill%5C%5C%5Cboxed%7Bx%5Cin%283%3B%2B%5Cinfty%29%7D%5Chfill%5C%5C%5Cend%7Bgathered%7D%5C%5D" title="\[\begin{gathered}2)\;\;{\log_{x-3}}(x+1)\hfill\\\left\{\begin{gathered}x+1>0\hfill\\x-3>0\hfill\\x-3\ne1\hfill\\\end{gathered}\right.\Leftrightarrow\left\{\begin{gathered}x>-1\hfill\\x>3\hfill\\x\ne4\hfill\\\end{gathered}\right.\hfill\\\boxed{x\in(3;+\infty)}\hfill\\\end{gathered}\]">
5^(x-2) = 5^0 2^(x² -3x +8) = 2^6
x-2 = 0 x² -3x +8 = 6
x = 2 x² -3x +2 = 0
2) 3·4^x =48 x = 1 и х = 2
4^x = 16 6)7^(2x-8)·7^(x+7) = 0
4^x = 4² нет решений
x=2 7)(0,2)^x ≤ 25·5√5
3)3^x=27·3√9 5^-x ≤ 5²·5·5^1/2
3^x = 3³·3·3 5^-x ≤5^3,5
3^x = 3^5 -x ≤ 3,5
x = 5 x ≥ -3,5
4)3^x + 3^(x +1) = 4 8)(1/2)^-x + 2^(3 +x) ≤9
3^x(1 +3) = 4 2^x +2^(3 +x) ≤ 9
3^x·4 = 4 2^x(1 +2^3) ≤ 9 | :9
3^x = 1 2^x ≤ 1
x = 0 2^x ≤2^0
x≤ 0