Question

Log3(5x-2)>1 log0,3(5x-2)>1 log5(x^2-11x+43)>2

Answer 1

Ответ 10 но это у меня так получилось

Answer 2

1)log3(5x-2)>1     одз:5x-2>0
 5x-2>3                      5x>2
 5x>5                         x>0.4
 x>1 
ответ:(1;+∞)       
2) log0,3(5x-2)>1   одз:5x-2>0
  5x-2 <0.3;                 5x>2
  5x<2.3                      x>0.4
  x<0.46 
 ответ:(0.4;0.46)
3)log5(x^2-11x+43)>2  x²-11x+43>0
 x²-11x+43>25            xɛR
 x²-11x+18>0
 x²-11x+18=0
 D=121- 72=49
 x1=(11-7)/2=2
 x2=(11+7)/2= 9
 (x-2)(x-9)>0
применяем метод интервалов 
  +           -            +
-------2--------------9--------
 ответ:(- ∞;2)(9;+ ∞)

  

Answer 3

To solve the inequalities involving logarithmic expressions, we need to apply the properties of logarithms and solve for the variable x. Let's work through each inequality step by step:

1. log₃(5x - 2) > 1:

To solve this inequality, we'll rewrite it in exponential form: 3¹ > 5x - 2 3 > 5x - 2 5x - 2 < 3 5x < 5 x < 1

Therefore, the solution to the inequality log₃(5x - 2) > 1 is x < 1.

2. log₀,₃(5x - 2) > 1:

Note that log₀,₃(5x - 2) is undefined because the base (0.3) is less than 1. Logarithms with a base less than 1 are not defined for positive values. Hence, this inequality has no solution.

3. log₅(x² - 11x + 43) > 2:

We'll rewrite the inequality in exponential form: 5² > x² - 11x + 43 25 > x² - 11x + 43 x² - 11x + 43 < 25 x² - 11x + 43 - 25 < 0 x² - 11x + 18 < 0

To solve this inequality, we can factorize the quadratic equation: (x - 2)(x - 9) < 0

Now we consider the sign of each factor:

x - 2 < 0 => x < 2 x - 9 < 0 => x < 9

To determine where the product is negative, we can create a sign chart:

markdownCopy code
  -       2       9      +

Now we need to find the solution within the intervals where the product is negative. From the chart, we see that x should be between 2 and 9 (exclusive) for the inequality to hold.

Therefore, the solution to log₅(x² - 11x + 43) > 2 is 2 < x < 9.

Please note that when working with logarithmic inequalities, we need to be cautious about the domain restrictions and potential extraneous solutions.