Question

Lg(11-3x) < 2-lg5 reshite pozhaluista

Answer 1

ОДЗ: 11-3x>0, 3x<11, x<11/3
lg(11-3x)<2lg(10)-lg5
lg(11-3x)<lg(100/5)
11-3x<20
3x>-9
x>-3
Ответ: х∈(-3;11/3)

Answer 2

To solve the inequality lg(11-3x) < 2 - lg5, we need to follow these steps:

Step 1: Combine logarithms on the right side of the inequality using the properties of logarithms. Step 2: Simplify the inequality as much as possible. Step 3: Solve for x.

Step 1: lg(11-3x) < 2 - lg5

Step 2: To combine the logarithms on the right side, we can use the logarithmic identity log(a) - log(b) = log(a/b):

lg(11-3x) + lg5 < 2

Step 3: Now, we can use the logarithmic property that states log(a) + log(b) = log(a * b):

lg(5 * (11-3x)) < 2

Now, let's eliminate the logarithm by converting the inequality into an exponent form:

5 * (11-3x) < 10^2

Simplify the right side:

5 * (11-3x) < 100

Now, let's continue solving for x:

Distribute the 5 on the left side:

55 - 15x < 100

Subtract 55 from both sides:

-15x < 45

Divide by -15 (note that we are dividing by a negative number, so the inequality sign flips):

x > -3

So, the solution to the inequality is x > -3.