Summer school and annual courses for the Unified State Exam 2025 with an MSU mathematician: https://3.shkolkovo.online/math-msu My Telegram channel: https://t.me/mathmsu Materials for the SIROP intensive course are here: https://mnlp.cc/mini?domain=mathmsu&i... If you are in the 10th grade, then this is where you should go: https://t.me/+yeAlGTQAn5E0ZmZi Everything about the MSU DWI is here: https://t.me/+hNmZJa59rY9hMjli VK group: https://vk.com/hitman_math Tik-Tok: / hitman_math My Instagram: / andreypavlikov_math Time codes: 00:00 Greeting and connection check 00:20 Syrup mini 02:37 Meeting the teacher 03:23 Intensive course schedule 03:56 Topic and lesson plan 05:06 Types of inequalities on the Unified State Exam 05:46 Graph of an exponential function 07:11 Properties of an exponential function 08:11 Basic exponential inequality 09:32 Graph of a logarithmic function 11:30 OED of a logarithmic function 12:10 Answers to questions 13:31 Methods for solving inequalities 14:11 Interval method 19:18 Answers to questions 22:50 Rationalization method 25:29 Answers to questions 26:48 Solving an inequality without the rationalization method 31:10 Answers to questions 34:53 Top preparatory course 36:15 Problem 1 - exponential inequality with radicals 37:18 Problem 1 - OED 38:30 Problem 1 - properties of powers and transformations 49:41 Answers to questions 55:09 Problem 2 - logarithmic inequality 56:01 Problem 2 - DQG 57:08 Problem 2 - transformation of the first logarithm 58:46 Answers to questions 59:43 Problem 2 - transformation of the second logarithm 1:01:31 Problem 2 - application of the substitution method 1:04:30 Problem 2 - back substitution and the first case 1:07:29 Problem 2 - interval method 1:10:21 Problem 2 - back substitution and the second case 1:13:35 Problem 2 - interval method 1:16:06 Answers to questions 1:20:42 Problem 3 - logarithmic inequality and the denominator 1:22:56 Problem 3 - DQG 1:27:28 Answers to questions 1:30:31 Problem 3 - transformation of the inequality on DQG 1:34:20 Answers to questions 1:40:37 Problem 3 - Answer on the number line 1:41:24 Breaking Bad 1:42:08 Problem 4 - Exponential inequality with moduli 1:45:12 Problem 4 - Logarithm of both sides of the inequality 1:45:59 Problem 4 - Transformation of the inequality 1:49:26 Answers to questions 1:51:33 Problem 4 - Cases of the value of the modulus 1:54:00 Answers to questions 2:03:38 Problem 5 - Exponential inequality and the denominator 2:04:09 Problem 5 - ODD 2:05:16 Problem 5 - Application of the substitution method 2:07:23 Problem 5 - Inverse substitution 2:11:00 Answers to questions 2:18:01 Problem 6 - Logarithms and trigonometry 2:20:25 Problem 6 - ODE 2:26:02 Problem 6 - comparing tangent with unity 2:30:26 Problem 6 - inequality transformation 2:31:56 Problem 6 - interval method 2:33:47 Answers to questions 2:37:01 Problem 7 - mixed inequality 2:39:05 Problem 7 - ODE 2:42:58 Problem 7 - inequality transformation 2:45:03 Problem 7 - numerator and denominator zeros 2:49:08 Problem 7 - interval method 2:54:23 Answers to questions 2:59:23 Problem 8 - logarithms and modules 3:03:04 Summary of the lesson and answers to questions #ege2024 #ode #inequalities USE 2024 USE in Mathematics Profile USE Typical examination options 36 options Preparation for the profile Unified State Exam in Mathematics Problem 15 Second part Complex inequalities Powers Logarithm Rational inequality Exponential inequality Logarithmic inequality Mixed inequalities Formulas for powers Formulas for logarithms Inequality with modulus Factorization Reduction to the simplest Substitution method Comparison of numbers ODE Range of admissible values ​​Interval method Rationalization method