Question

Log3^2 x – log3 x >0

Answer 1

Ответ:

Пошаговое объяснение:

ОДЗ: x>0

log3(x)=t

t²-t>0

t∈(-∞;0)∪(1;+∞)

log3(x)<0

log3(x)>1

x<1

x>3

Ответ: x∈(0;1)∪(3;+∞)

Answer 2

Ответ:

( 3; +∞)

Пошаговое объяснение:

log²₃x – log₃x > 0

x > 0

log₃x = y

y² - y > 0

y (y - 1) > 0

y < 0 или y > 1

log₃x < 0 или log₃x > 1

log₃x < log₃1 или log₃x > log₃3

x < 1 или x > 3

Ответ: x ∈ (0; 1) ∪ ( 3; +∞)

Answer 3

To solve the inequality $\log_3^2 x - \log_3 x > 0$, we can use logarithm properties to simplify it. Remember that $\log_a^n b = n \cdot \log_a b$.

Let's work through the inequality step by step:

$\log_3^2 x - \log_3 x > 0$

Using the logarithm property:

$2 \cdot \log_3 x - \log_3 x > 0$

Combine the logarithms:

$\log_3 x > 0$

Now, we have a single logarithm expression greater than 0. The domain of a logarithm with a positive argument is all positive real numbers. Thus, the solution to the inequality is:

$x > 1$

So, the inequality $\log_3^2 x - \log_3 x > 0$ is satisfied when $x$ is greater than 1.